

A235634


Primes whose base4 representation is also the base7 representation of a prime.


2



2, 3, 11, 23, 29, 31, 41, 71, 79, 101, 109, 113, 137, 149, 157, 163, 191, 199, 239, 251, 263, 269, 283, 307, 353, 397, 401, 431, 443, 521, 547, 601, 701, 709, 743, 751, 773, 853, 887, 941, 947, 983, 1013, 1039, 1049, 1069, 1109, 1151, 1217, 1283, 1303, 1487, 1489, 1663, 1669, 1789, 1823, 1901, 1949, 1973
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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

Robert Israel, 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

E.g., 11 = 23_4 and 23_7 = 17 both are prime.


MAPLE

filter:= proc(n) local L, m;
if not isprime(n) then return false fi;
L:= convert(n, base, 4);
isprime(add(L[i]*7^(i1), i=1..nops(L)));
end proc:
select(filter, [2, seq(i, i=3..10000, 2)]); # Robert Israel, Jul 02 2018


PROG

(PARI) is(p, b=7, c=4)=isprime(vector(#d=digits(p, c), i, b^(#di))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.


CROSSREFS

Cf. A235617, 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: A229805 A104075 A236168 * A070174 A320393 A080153
Adjacent sequences: A235631 A235632 A235633 * A235635 A235636 A235637


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 13 2014


STATUS

approved



