A235464 Primes whose base-7 representation also is the base-2 representation of a prime.

7, 2801, 17207, 19559, 134513, 134807, 840743, 842759, 842801, 941249, 943601, 958007, 958049, 958343, 5899657, 6591089, 6607903, 6706393, 6722857, 41196751, 41311663, 41314057, 46137673, 46137967, 46253257, 46942351, 46944409, 47059657

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=7, thus a subsequence of A077721.

Links

Table of n, a(n) for n=1..28.

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

Example

7 = 10_7 and 10_2 = 2 are both prime, so 7 is a term.
2801 = 11111_7 and 11111_2 = 31 are both prime, so 2801 is a term.

Prog

(PARI) is(p, b=2, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 7, 2)&&print1(vector(#d=digits(p, 2), i, 7^(#d-i))*d~, ", ")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(., 2, 7)

Crossrefs

Cf. A235477, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A195680 A203587 A077721 * A297029 A242851 A264787

Adjacent sequences: A235461 A235462 A235463 * A235465 A235466 A235467

Keyword

nonn,base

Author

M. F. Hasler, Jan 11 2014

Status

approved