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

Author

Antti Karttunen, Jun 12 2004

Keywords

• nonn
• base

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.)

Examples

			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.
		

Links

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

Crossrefs

Cf. A095758, A095749, A095743.

Programs

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,", ")))

Extensions

Edited by Washington Bomfim, Jan 13 2011