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

2, 3, 5, 7, 19, 37, 67, 79, 97, 103, 127, 157, 163, 193, 229, 283, 307, 337, 439, 487, 547, 571, 601, 631, 643, 673, 733, 751, 757, 853, 877, 907, 937, 1021, 1033, 1039, 1087, 1093, 1117, 1171, 1249, 1279, 1423, 1567, 1627, 1663, 1723, 1753, 1831, 1873

Offset

1,1

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

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

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, 6); if (isprime(b), write("b065724.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009
(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 6), 10)); \\ Michel Marcus, Mar 05 2022

Crossrefs

Cf. A065720 up to A065727, A065361.

Sequence in context: A288717 A144561 A215156 * A235620 A289756 A236303

Adjacent sequences: A065721 A065722 A065723 * A065725 A065726 A065727

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 2001

Status

approved