A091924 Primes such that their decimal representations interpreted in base 11 are also prime.

2, 3, 5, 7, 29, 43, 61, 67, 89, 139, 193, 197, 199, 227, 263, 269, 281, 331, 353, 373, 379, 467, 571, 601, 607, 643, 733, 797, 809, 821, 827, 887, 919, 937, 1033, 1039, 1093, 1129, 1231, 1237, 1259, 1277, 1303, 1327, 1381, 1451, 1453, 1459, 1583

Offset: 1

Author

Reinhard Zumkeller, Feb 13 2004

Keywords

• nonn
• base

Comments

See A090711 for a similar sequence whose definition works "in the opposite direction". - M. F. Hasler, Jan 03 2014

Examples

			A000040(10)=29 in base 11 is 2*11^1+9*11^0=31 prime, therefore 29 is a term.
		

Links

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

Crossrefs

Cf. A091923.

Programs

Magma

[n:n in PrimesUpTo(1600)| IsPrime(Seqint(Intseq(n),11))]; // Marius A. Burtea, Jun 30 2019

Maple

filter:= proc(n) local L;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  isprime(add(L[i]*11^(i-1),i=1..nops(L)))
end proc:
select(filter, [2, seq(i,i=3..10000,2)]); # Robert Israel, Jan 28 2018

Mathematica

Select[Prime@ Range@ 250, PrimeQ@ FromDigits[IntegerDigits@ #, 11] &] (* Michael De Vlieger, Aug 29 2015 *)

PARI

is(p,b=11)={my(d=digits(p));isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)} \\ M. F. Hasler, Jan 03 2014

Formula

A090862(A049084(a(n))) > 11 for n>4.

Extensions

Corrected by Zak Seidov, Feb 25 2004