| A001113 |
Decimal expansion of e. |
| A002487 |
Stern’s diatomic series. |
| A002708 |
a(n) = Fibonacci(n) mod n. |
| A003132 |
Sum of squares of digits of n. |
| A003986 |
Table of x OR y, where (x,y) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), … |
| A003987 |
Table of n XOR m (or Nim-sum of n and m) read by antidiagonals, i.e., with entries in the order (n,m) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), … |
| A003991 |
Multiplication table read by antidiagonals: T(i,j) = i*j, i>=1, j>=1. |
| A004185 |
Arrange digits of n in increasing order, then (for n>0) omit the zeros. |
| A004186 |
Arrange digits of n in decreasing order. |
| A004198 |
Table of x AND y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),… |
| A005590 |
a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1) - a(n). |
| A006577 |
Number of halving and tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached. |
| A007305 |
Numerators of Farey (or Stern-Brocot) tree fractions. |
| A007434 |
Jordan function J_2(n) (a generalization of phi(n)). |
| A008330 |
phi(p-1), as p runs through the primes. |
| A030101 |
a(n) is the number produced when n is converted to binary digits, the binary digits are reversed and then converted back into a decimal number. |
| A030102 |
Base-3 reversal of n (written in base 10). |
| A036839 |
RATS(n): Reverse Add Then Sort the digits. |
| A037861 |
(Number of 0’s) - (number of 1’s) in the base-2 representation of n. |
| A046901 |
a(n) = a(n-1) - n if a(n-1) > n, else a(n) = a(n-1) + n. |
| A047679 |
Denominators in full Stern-Brocot tree. |
| A050873 |
Triangular array T read by rows: T(n,k) = gcd(n,k). |
| A052126 |
a(1) = 1; for n>1, a(n)=n/(largest prime dividing n). |
| A053222 |
First differences of sigma(n). |
| A056539 |
Self-inverse permutation: reverse the bits in binary expansion of n and also complement them (0->1, 1->0) if the run count (A005811) is even. |
| A057889 |
Bit-reverse of n, including as many leading as trailing zeros. |
| A059893 |
Reverse the order of all but the most significant bit in binary expansion of n: if n = 1ab..yz then a(n) = 1zy..ba. |
| A063114 |
n + product of nonzero digits of n. |
| A064989 |
Multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes. |
| A065075 |
Sum of digits of the sum of the preceding numbers. |
| A065620 |
a(0)=0; thereafter a(2n) = 2a(n), a(2n+1) = -2a(n) + 1. |
| A066520 |
Number of primes of the form 4m+3 <= n minus number of primes of the form 4m+1 <= n. |
| A073138 |
Largest number having in its binary representation the same number of 0’s and 1’s as n. |
| A087909 |
a(n) = Sum_{d|n} (n/d)^(d-1). |
| A093873 |
Numerators in Kepler’s tree of harmonic fractions. |
| A129594 |
Involution of nonnegative integers induced by the conjugation of the partition encoded in the run lengths of binary expansion of n. |
| A151949 |
a(n) = image of n under the Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order). |
| A155043 |
a(0)=0; for n >= 1, a(n) = 1 + a(n-d(n)), where d(n) is the number of divisors of n (A000005). |
| A160595 |
Numerator of resilience R(n) = phi(n)/(n-1), with a(1) = 1 by convention. |
| A175851 |
a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n. |
| A186690 |
Expansion of - (1/8) theta_3’’(0, q) / theta_3(0, q) in powers of q. |
| A220466 |
a((2*n-1)*2^p) = 4^p*(n-1) + 2^(p-1)*(1+2^p), p >= 0 and n >= 1. |
| A227183 |
a(n) is the sum of parts of the unique unordered partition encoded in the run lengths of the binary expansion of n; row sums of A227739 for n >= 1. |
| A243499 |
Product of parts of integer partitions as enumerated in the table A125106. |
| A276086 |
Prime product form of primorial base expansion of n: digits in primorial base representation of n become the exponents of successive prime factors whose product a(n) is. |
| A276150 |
Sum of digits when n is written in primorial base (A049345); minimal number of primorials (A002110) that add to n. |
| A289813 |
A binary encoding of the ones in ternary representation of n. |
| A289814 |
A binary encoding of the twos in ternary representation of n. |
| A306367 |
a(n) = numerator of (n^2 + 2)/(n + 2). |
| A318458 |
a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors. |
| A328572 |
Primorial base expansion of n converted into its prime product form, but with 1 subtracted from all nonzero digits: a(n) = A003557(A276086(n)). |
| A336466 |
Fully multiplicative with a(p) = A000265(p-1) for any prime p, where A000265(k) gives the odd part of k. |
| A340649 |
a(n) = (n*prime(n+1)) mod prime(n). |
| A342730 |
a(n) = floor((frac(e*n) + 1) * prime(n+1)). |
