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

1,1

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.

Links

Table of n, a(n) for n=1..44.

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.)

Example

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

Prog

(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))}

Crossrefs

Cf. A090418, A090421, A090423, A257318.

Sequence in context: A187773 A328825 A107662 * A276435 A083370 A124582

Adjacent sequences: A256869 A256870 A256871 * A256873 A256874 A256875

Keyword

nonn,base

Author

M. F. Hasler, Apr 21 2015

Status

approved