A279052 Semiprimes whose binary and ternary representations are prime when read in decimal.

295, 1189, 2515, 4399, 4897, 5137, 7045, 7261, 7999, 8065, 9019, 9637, 10579, 10951, 10963, 11035, 11233, 12679, 13315, 13603, 13849, 16279, 18295, 20065, 20467, 20497, 23089, 23419, 23551, 23983, 26359, 27007, 27301, 27787, 29647, 33127, 33253, 33763, 34189, 34411

Offset

1,1

Links

K. D. Bajpai and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 4075 terms from K. D. Bajpai)

Example

295 is in the sequence because 295 = 5*59 (semiprime), 295_10 = 100100111_2 = 101221_3, and both 100100111_10 and 101221_10 are prime.
1189 is in the sequence because 1189 = 29*41 (semiprime), and both its binary representation 10010100101 and its ternary representation 1122001, if read as decimal numbers, are prime.

Mathematica

Select[Range[50000], PrimeOmega[#] == 2 && PrimeQ[FromDigits[IntegerDigits[#, 2]]] && PrimeQ[FromDigits[IntegerDigits[#, 3]]] &]

Prog

(PARI) has(n, b)=isprime(fromdigits(digits(n, b), 10))
list(lim)=my(v=List(), t); forprime(p=2, lim\2, forprime(q=2, min(lim\p, p), if(has(t=p*q, 2) && has(t, 3), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Dec 05 2016

Crossrefs

Subsequence of A001358.

Cf. A000040, A007089, A036952, A065720, A236365, A236537.

Sequence in context: A074868 A277338 A252083 * A237803 A238512 A003780

Adjacent sequences: A279049 A279050 A279051 * A279053 A279054 A279055

Keyword

nonn,base

Author

K. D. Bajpai, Dec 05 2016

Status

approved