A235126 Primes whose base-10 representation also represents a prime in base 17.

2, 3, 5, 7, 23, 29, 43, 61, 67, 83, 137, 139, 191, 197, 227, 241, 263, 313, 331, 461, 577, 593, 599, 607, 683, 739, 821, 863, 937, 953, 1013, 1033, 1039, 1051, 1297, 1303, 1327, 1459, 1619, 1693, 1721, 1787, 1811, 1877, 1949

Offset: 1

Author

M. F. Hasler, Jan 03 2014

Keywords

• nonn
• base

Comments

See A090713 for a similar sequence whose definition works "in the opposite direction".

Examples

			The decimal representation of prime 23, considered as a number written in base 17, stands for 2*17+3 = 37, which is also prime, therefore 23 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A235110 and other sequences in the range A090707 - A091924.

Programs

Maple

filter:= proc(p) local L;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  isprime(add(L[i]*17^(i-1),i=1..nops(L)))
end proc:
select(filter, [2,seq(i,i=3..10000,2)]); # Robert Israel, Apr 25 2017

Mathematica

Select[Prime@ Range@ 300, PrimeQ@ FromDigits[IntegerDigits@ #, 17] &] (* Michael De Vlieger, Jan 03 2016 *)

PARI

is(p, b=17)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows the production of similar sequences for other bases b > 9 (which can be given as an optional 2nd argument), but does not do the required check for bases b < 10.