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 A065725 Primes p such that the decimal expansion of its base-7 conversion is also prime. 5
 2, 3, 5, 17, 29, 31, 43, 59, 71, 127, 157, 197, 211, 227, 239, 241, 337, 353, 367, 379, 409, 463, 491, 563, 577, 619, 647, 743, 757, 773, 787, 857, 911, 953, 967, 1093, 1123, 1163, 1193, 1249, 1303, 1373, 1429, 1459, 1471, 1499, 1583, 1597, 1613, 1627, 1669 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In general rebase notation (Marc LeBrun): p7 = (7) [p] (10). LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 EXAMPLE E.g., 787_10 = 2203_7 is prime, and so is 2203_10. MATHEMATICA Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 7]]] & ] Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 7]]]&] (* Harvey P. Dale, Nov 10 2022 *) 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, 7); if (isprime(b), write("b065725.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009 (PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 7), 10)); \\ Michel Marcus, Mar 05 2022 CROSSREFS Cf. A065720 up to A065727, A065361. Sequence in context: A127061 A215311 A215315 * A057468 A127062 A214735 Adjacent sequences: A065722 A065723 A065724 * A065726 A065727 A065728 KEYWORD nonn,base AUTHOR Patrick De Geest, Nov 15 2001 STATUS approved

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Last modified June 9 06:42 EDT 2023. Contains 363168 sequences. (Running on oeis4.)