

A235636


Primes whose base6 representation is also the base7 representation of a prime.


2



2, 3, 5, 17, 47, 71, 97, 101, 131, 157, 173, 191, 211, 251, 257, 277, 307, 311, 353, 367, 401, 421, 461, 487, 491, 563, 577, 601, 631, 643, 647, 683, 701, 743, 751, 761, 853, 857, 907, 911, 937, 953, 983, 1021, 1033, 1087, 1103, 1193, 1201, 1259, 1277, 1289, 1327, 1451, 1471, 1571, 1583, 1597, 1601, 1747, 1831, 1907, 1933
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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

Harvey P. Dale, Table of n, a(n) for n = 1..1000
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime


EXAMPLE

17 = 25_6 and 25_7 = 19 are both prime.


MATHEMATICA

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 6], 7]]&] (* Harvey P. Dale, Sep 17 2017 *)


PROG

(PARI) is(p, b=7, c=6)=isprime(vector(#d=digits(p, c), i, b^(#di))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.


CROSSREFS

Cf. A235637, A235265, A235266, A152079, A235461  A235482, A065720  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235615  A235639. See the LINK for further crossreferences.
Sequence in context: A256426 A019350 A235630 * A268130 A103074 A173236
Adjacent sequences: A235633 A235634 A235635 * A235637 A235638 A235639


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 13 2014


STATUS

approved



