A095748 Almost maximally asymmetric primes in binary.

17, 31, 37, 41, 47, 59, 61, 67, 89, 97, 103, 139, 149, 163, 197, 263, 269, 283, 293, 307, 353, 359, 379, 389, 409, 433, 439, 449, 461, 499, 541, 557, 607, 613, 631, 659, 727, 743, 809, 829, 877, 929, 941, 953, 997, 1009, 1039, 1051, 1151, 1171

Offset

1,1

Comments

Primes p for which A037888(p) = floor((A070939(p)-4)/2). Those numbers contain just two bits mirroring each other, beyond the first and last bits. (All the odd primes without leading zeros begin and end in 1 bits.)

Links

Table of n, a(n) for n=1..50.

A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence

Example

a(5)=(101111)2. In this case, from left to right, the third bit agrees with the fourth. The prime 53 = (110101)_2 is not a term since the symmetry is limited to the first and last bits.

Prog

(PARI) A070939(p) = { return(floor(log(p)/log(2))+1) };
A037888(p)={v=binary(p); s=0; j=#v; for(k=1, #v, s+=abs(v[k]- v[j]); j--); return(s/2); }; forprime(p=3, 1171, if(A037888(p)==floor((A070939(p)-4)/2), print1(p, ", ")))

Crossrefs

Cf. A095758, A095749, A095743.

Sequence in context: A002675 A333855 A321217 * A350699 A235920 A268923

Adjacent sequences: A095745 A095746 A095747 * A095749 A095750 A095751

Keyword

nonn,base

Author

Antti Karttunen, Jun 12 2004

Extensions

Edited by Washington Bomfim, Jan 13 2011

Status

approved