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 A065727 Primes p such that the decimal expansion of its base-9 conversion is also prime. 75
 2, 3, 5, 7, 37, 43, 61, 109, 127, 199, 271, 277, 379, 457, 487, 523, 541, 613, 619, 673, 727, 757, 883, 907, 919, 991, 997, 1033, 1117, 1249, 1447, 1483, 1531, 1549, 1567, 1627, 1693, 1699, 1747, 1753, 1987, 2053, 2161, 2221, 2287, 2341, 2347, 2437, 2473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In general rebase notation (Marc LeBrun): p9 = (9) [p] (10). LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 EXAMPLE E.g., 997_10 = 1327_9 is prime, and so is 1327_10. MATHEMATICA Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ] NestList[NestWhile[NextPrime, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 9]]] &, 2] &, 2, 48] (* Jan Mangaldan, Jul 01 2020 *) Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 9], 10]]&] (* Harvey P. Dale, Sep 19 2021 *) PROG (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 (PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 9))); \\ Michel Marcus, Jul 02 2020 CROSSREFS Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065361. Intersection of A000040 and A036964. Sequence in context: A274678 A048415 A029974 * A090713 A090912 A048416 Adjacent sequences: A065724 A065725 A065726 * A065728 A065729 A065730 KEYWORD nonn,base AUTHOR Patrick De Geest, Nov 15 2001 STATUS approved

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Last modified September 25 18:27 EDT 2023. Contains 365648 sequences. (Running on oeis4.)