%I #22 Mar 05 2022 11:09:05

%S 2,3,5,7,37,43,61,109,127,199,271,277,379,457,487,523,541,613,619,673,

%T 727,757,883,907,919,991,997,1033,1117,1249,1447,1483,1531,1549,1567,

%U 1627,1693,1699,1747,1753,1987,2053,2161,2221,2287,2341,2347,2437,2473

%N Primes p such that the decimal expansion of its base-9 conversion is also prime.

%C In general rebase notation (Marc LeBrun): p9 = (9) [p] (10).

%H Harry J. Smith, <a href="/A065727/b065727.txt">Table of n, a(n) for n = 1..1000</a>

%e E.g., 997_10 = 1327_9 is prime, and so is 1327_10.

%t Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ]

%t NestList[NestWhile[NextPrime, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 9]]] &, 2] &, 2, 48] (* _Jan Mangaldan_, Jul 01 2020 *)

%t Select[Prime[Range[400]],PrimeQ[FromDigits[IntegerDigits[#,9],10]]&] (* _Harvey P. Dale_, Sep 19 2021 *)

%o (PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 9); if (isprime(b), write("b065727.txt", n++, " ", p); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 28 2009

%o (PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 9))); \\ _Michel Marcus_, Jul 02 2020

%Y Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065361.

%Y Intersection of A000040 and A036964.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 2001