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

Author

Zak Seidov, Jun 12 2005

Keywords

• nonn
• base

Comments

34 is the smallest term in common with A108605.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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