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A108606
Semiprimes with prime sum of digits.
4
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
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Jun 12 2005
STATUS
approved