A231477 - OEIS

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A231477

Primes whose base-3 representation is also the base-7 representation of a prime.

2, 3, 23, 41, 47, 53, 61, 67, 71, 89, 113, 127, 131, 137, 191, 193, 223, 251, 269, 283, 293, 311, 353, 397, 409, 421, 443, 463, 491, 503, 509, 541, 569, 601, 613, 701, 773, 787, 983, 1013, 1031, 1091, 1117, 1213, 1223, 1429, 1499, 1543, 1549, 1579, 1619, 1621, 1697, 1699, 1733, 1873, 1933, 1949, 1951, 1973

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This sequence is part of a two-dimensional array of sequences, given in the LINK, 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.

LINKS

Giovanni Resta, 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

23 = 212_3 and 212_7 = 107 are both prime, so 23 is a term.

MATHEMATICA

Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 3], 7] &] (* Giovanni Resta, Sep 12 2019 *)

PROG

(PARI) is(p, b=7, c=3)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

CROSSREFS

Cf. A235470, A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.

Sequence in context: A176892 A109615 A101001 * A215325 A215353 A215305

Adjacent sequences: A231474 A231475 A231476 * A231478 A231479 A231480

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 12 2014

STATUS

approved