A108606 Semiprimes with prime sum of digits.

14, 21, 25, 34, 38, 49, 58, 65, 74, 85, 94, 106, 111, 115, 119, 122, 133, 142, 146, 155, 166, 201, 203, 205, 209, 214, 218, 221, 247, 254, 265, 274, 278, 287, 289, 298, 302, 319, 326, 335, 346, 355, 362, 371, 377, 382, 386, 391, 395, 403, 407, 427, 445, 454

Offset

1,1

Comments

34 is the smallest term in common with A108605.

Links

J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..10000

Example

34 = 2*17 (semiprime) and 2 + 17 = 19 is prime.

Mathematica

A108606=Select[Range[1000], Plus@@(Transpose[FactorInteger[ # ]])[[2]]==2&& PrimeQ[Plus@@IntegerDigits[ # ]]&]
DeleteCases[ParallelTable[If[PrimeOmega[n]==2&&PrimeQ[Total[IntegerDigits[n]]], n, a], {n, 0, 126181}], a] (* J.W.L. (Jan) Eerland, Dec 21 2021 *)

Prog

(PARI) select(isA108606(n)={bigomega(n)==2&&isprime(sumdigits(n))}, [1..1000]) \\ J.W.L. (Jan) Eerland, Dec 23 2021
(Python)
from sympy import isprime, factorint
def ok(n): return isprime(sum(map(int, str(n)))) and sum(factorint(n).values()) == 2
print([k for k in range(455) if ok(k)]) # Michael S. Branicky, Aug 22 2022

Crossrefs

Cf. A001358 (semiprimes), A101605 (3-almost primes), A108605 (semiprimes with prime sum of factors), A108607 (intersection of A108605 and A108606).

Sequence in context: A234802 A162780 A002410 * A129497 A255742 A093994

Adjacent sequences: A108603 A108604 A108605 * A108607 A108608 A108609

Keyword

nonn,base

Author

Zak Seidov, Jun 12 2005

Status

approved