A294994 Begin with 2; thereafter a(n) is the least prime not already in the sequence such that the Hamming distance between it and the preceding prime is at most 2.

2, 3, 5, 7, 11, 13, 29, 17, 19, 23, 31, 47, 37, 41, 43, 59, 61, 53, 101, 71, 67, 73, 79, 103, 97, 107, 109, 127, 191, 151, 131, 137, 139, 163, 167, 173, 157, 149, 181, 179, 211, 83, 89, 113, 241, 193, 197, 199, 223, 239, 227, 229, 233, 251, 379, 283, 271, 263, 257, 269, 277, 281, 313, 307, 311, 293

Offset

1,1

Comments

The Hamming distance between two primes p and q is the Hamming distance between their binary expansions. - N. J. A. Sloane, May 27 2018

Conjecture: this sequence is a permutation of the primes.

By definition, the absolute difference of a(n) and a(n + 1) is in A048645. - David A. Corneth, Jan 12 2018

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of (x, y) such that the prime numbers prime(x) and prime(y) have Hamming distance <= 2 for x = 1..1000 and y = 1..1000

Mathematica

f[s_List] := Block[{p = s[[-1]], q = 3}, While[MemberQ[s, q] || Plus @@ IntegerDigits [BitXor[p, q], 2] > 2, q = NextPrime@q]; Append[s, q]]; s = {2}; Nest[f, s, 65]

Prog

(PARI) s = 0; v = 2; for (n=1, 66, print1 (v ", "); s += 2^v; forprime (p=2, oo, if (!bittest(s, p) && hammingweight(bitxor(p, v))<=2, v = p; break))) \\ Rémy Sigrist, Jan 08 2018

Crossrefs

Cf. A000040, A004676, A048645, A163252.

See also A303593, A303594, A303595 (when n-th prime appears).

Sequence in context: A024694 A024320 A265885 * A292205 A111252 A181525

Adjacent sequences: A294991 A294992 A294993 * A294995 A294996 A294997

Keyword

nonn,base

Author

Robert G. Wilson v, Nov 12 2017

Status

approved