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A065724 Primes p such that the decimal expansion of its base-6 conversion is also prime. 5

%I #15 Mar 05 2022 11:08:48

%S 2,3,5,7,19,37,67,79,97,103,127,157,163,193,229,283,307,337,439,487,

%T 547,571,601,631,643,673,733,751,757,853,877,907,937,1021,1033,1039,

%U 1087,1093,1117,1171,1249,1279,1423,1567,1627,1663,1723,1753,1831,1873

%N Primes p such that the decimal expansion of its base-6 conversion is also prime.

%C In general rebase notation (Marc LeBrun): p6 = (6) [p] (10).

%H Harry J. Smith, <a href="/A065724/b065724.txt">Table of n, a(n) for n = 1..1000</a>

%e E.g., 1627_10 = 11311_6 is prime, and so is 11311_10.

%t Select[ Range[1900], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 6]]] & ]

%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, 6); if (isprime(b), write("b065724.txt", n++, " ", p); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 27 2009

%o (PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 6), 10)); \\ _Michel Marcus_, Mar 05 2022

%Y Cf. A065720 up to A065727, A065361.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 2001

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)