A090421 Numbers that can be written in binary representation as concatenation of primes.

2, 3, 5, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 29, 30, 31, 37, 41, 42, 43, 45, 46, 47, 53, 54, 55, 58, 59, 61, 62, 63, 67, 70, 71, 73, 78, 79, 81, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 101, 103, 107, 109, 111, 113, 115, 117, 118, 119, 122, 123

Offset: 1

Author

Reinhard Zumkeller, Nov 30 2003

Keywords

• nonn
• base

Comments

A090418(a(n)) > 0; complement of A090419.

Terms in the sequence cannot end in 00, 0010, 001010, etc., and thus a(n) > 3n/2 + O(log n). - Charles R Greathouse IV, Apr 21 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004676, A007088, A090422.

Cf. A000040, A090420, and A090423 are subsequences.

Programs

Haskell

a090421 n = a090421_list !! (n-1)
a090421_list = filter ((> 0) . a090418) [1..]
-- Reinhard Zumkeller, Aug 06 2012

PARI

is_A090421(n)={isprime(n) || if(bittest(n,0),for(k=2,#binary(n)-2,bittest(n,k-1) && isprime(n%2^k) && is_A090421(n>>k) && return(1)), bittest(n,1) && is_A090421(n>>2))} \\ Charles R Greathouse IV and M. F. Hasler, Apr 21 2015

Extensions

Based on corrections in A090418, data recomputed by Reinhard Zumkeller, Aug 06 2012