A090711 - OEIS

%I #23 Nov 02 2023 23:41:37

%S 2,3,5,7,31,47,67,73,97,163,223,227,229,271,311,317,331,397,421,443,

%T 449,557,683,727,733,773,883,953,977,991,997,1063,1109,1129,1367,1373,

%U 1433,1483,1607,1613,1637,1657,1697,1723,1783,1871,1873,1879,2027,2203,2269

%N Primes whose base-11 expansion is a (valid) decimal expansion of a prime.

%C See A091924 for the sequence whose definition works "the other way round": Actually, the base-11 representation of the terms of this sequence here. - _M. F. Hasler_, Jan 03 2014

%H Robert Price, <a href="/A090711/b090711.txt">Table of n, a(n) for n = 1..19838</a>

%e The prime p = 31 is written 29 in base 11, and 29 read in base 10 is again a prime. So 31 is a term.

%t b11pQ[n_]:=Module[{d=IntegerDigits[n,11]},Max[d]<10&&PrimeQ[FromDigits[ d]]]; Select[Prime[Range[400]],b11pQ] (* _Harvey P. Dale_, Apr 17 2018 *)

%o (PARI) is(p,b=10,c=11)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p) \\ _M. F. Hasler_, Jan 05 2014

%Y Cf. A090712.

%K base,nonn

%O 1,1

%A _Cino Hilliard_, Jan 18 2004

%E Edited by _N. J. A. Sloane_, Feb 07 2007, and by _M. F. Hasler_, Jan 03 2014