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

1,1

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.

Links

Table of n, a(n) for n=1..49.

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

Example

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.

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

Crossrefs

Cf. A095757, A095749, A095748.

Sequence in context: A079733 A179538 A216371 * A132779 A192869 A147513

Adjacent sequences: A095744 A095745 A095746 * A095748 A095749 A095750

Keyword

nonn,base

Author

Antti Karttunen, Jun 12 2004

Extensions

Edited by Washington Bomfim, Jan 13 2011

Status

approved