A235465 Primes whose base-8 representation also is the base-2 representation of a prime.

73, 521, 577, 4673, 32833, 33289, 33353, 36929, 37441, 262153, 262217, 262657, 295433, 2097673, 2101313, 2359369, 2363401, 2392073, 16777289, 16810049, 16814089, 16814153, 16814657, 17039881, 17043977, 17076809, 18874433, 18907201, 19137089, 19140617, 134222401, 134483969, 134484481, 134513161

Offset

1,1

Comments

This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=8, thus a subsequence of A077722.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Example

73 = 111_8 and 111_2 = 7 are both prime, so 73 is a term.

Prog

(PARI) is(p, b=2, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 8, 2)&&print1(vector(#d=digits(p, 2), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(., 2, 8)

Crossrefs

Cf. A235478, A235479, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A043427 A038485 A077722 * A201263 A210390 A210383

Adjacent sequences: A235462 A235463 A235464 * A235466 A235467 A235468

Keyword

nonn,base

Author

M. F. Hasler, Jan 11 2014

Status

approved