A256872 Numbers whose binary expansion is the concatenation of the binary expansion of two prime numbers in at least two ways.

23, 31, 45, 47, 61, 93, 95, 119, 125, 127, 175, 187, 189, 191, 239, 247, 253, 255, 335, 357, 359, 363, 369, 379, 381, 383, 431, 439, 455, 477, 485, 491, 493, 495, 507, 509, 511, 573, 575, 631, 637, 639, 669, 671

Offset: 1

Author

M. F. Hasler, Apr 21 2015

Keywords

• nonn
• base

Comments

A simplified variant (and subsequence) of A257318 (and A090421) where the concatenation of any number of primes is considered.

The subsequence of numbers which are concatenation of 2 primes in at least 3 ways is (93, 95, 189, 191, 239, 253, 335, 381, 383, 669, ...).

All terms are odd. Indeed, if an even number n > 2 is concatenation of two primes (in binary), then it is of the form 'n' = 'floor(n/4)''2' (where 'x' is x in binary), and there is no other possible decomposition.

Examples

			23 = 10111[2] = (10[2])(111[2]) = (101[2])(11[2]) which is (2)(7) resp. (5)(3).
		

Crossrefs

Cf. A090418, A090421, A090423, A257318.

Programs

PARI

is(n,c=2)={for(i=2,#binary(n)-2,bittest(n,i-1)&&isprime(n>>i)&&isprime(n%2^i)&&!c--&&return(1))}

Formula

A090418(a(n)) >= 2. (Necessary but not sufficient condition. This actually characterizes elements of A257318. For example, all terms of A090423 satisfy this but many of them are not terms of this sequence.)