A091924 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

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

CROSSREFS

Cf. A091923.

Sequence in context: A332582 A019372 A117299 * A358382 A069108 A156604

Adjacent sequences: A091921 A091922 A091923 * A091925 A091926 A091927

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Feb 13 2004

EXTENSIONS

Corrected by Zak Seidov, Feb 25 2004

STATUS

approved