A095747 Maximally asymmetric odd primes in binary.

3, 5, 7, 11, 13, 19, 23, 29, 43, 53, 71, 79, 83, 101, 109, 113, 151, 179, 233, 241, 271, 311, 331, 347, 397, 421, 457, 599, 683, 739, 797, 853, 937, 977, 1087, 1103, 1223, 1307, 1427, 1459, 1597, 1613, 1733, 2017, 2111, 2143, 2503, 2731, 3011

Offset: 1

Author

Antti Karttunen, Jun 12 2004

Keywords

• nonn
• base

Comments

Primes p for which A037888(p) = floor((A070939(p)-2)/2). Those numbers contain just the first and last bits mirroring each other. Hence all the odd primes without leading zeros begin and end in 1 bits, the unique totally asymmetric prime being (10)_2 = 2.

Examples

			a(10)=(110101)2 since the symmetry is limited to the first and last bits. The number 47=(101111)2 is not a term because from left to right, the third bit matches with the fourth.
		

Links

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

Crossrefs

Cf. A095757, A095749, A095748.

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=3,3011, if(A037888(p) ==floor((A070939(p)-2)/2),print1(p,", ")))

Extensions

Edited by Washington Bomfim, Jan 13 2011