

A235464


Primes whose base7 representation also is the base2 representation of a prime.


1



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
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OFFSET

1,1


COMMENTS

This sequence is part of the twodimensional 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 crossreferences, 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^(#di))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 7, 2)&&print1(vector(#d=digits(p, 2), i, 7^(#di))*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 crossreferences.
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



