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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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.

Crossrefs

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

Sequence in context: A069556 A210110 A235144 * A309248 A267014 A113611

Adjacent sequences: A235123 A235124 A235125 * A235127 A235128 A235129

Keyword

nonn,base

Author

M. F. Hasler, Jan 03 2014

Status

approved