A108610 Semiprimes with prime sum of decimal digits and prime sum of prime factors.

34, 58, 142, 214, 274, 298, 382, 454, 478, 562, 694, 838, 922, 1042, 1138, 1198, 1282, 1318, 1642, 1714, 2038, 2098, 2122, 2182, 2302, 2458, 2638, 2854, 2902, 2962, 3334, 3394, 3442, 3574, 3754, 3862, 4054, 4162, 4258, 4474, 4618, 4762, 5314, 5374, 5422

Offset: 1

Author

Zak Seidov, Jun 12 2005

Keywords

• nonn
• base

Comments

Intersection of A108605 and A108606. All terms are even. Cf. A001358 semiprimes, A101605 3-almost primes, A108605 semiprimes with prime sum of factors, A108606 semiprimes with prime sum of digits.

Examples

			34=2*17 (semiprime), with 3+4=7 and 2+17=19 both prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A101605, A108605, A108606.

Programs

Mathematica

psddQ[n_]:=!IntegerQ[Sqrt[n]]&&PrimeOmega[n]==2&&PrimeQ[Total[ IntegerDigits[n]]] && PrimeQ[Total[Transpose[FactorInteger[n]][[1]]]]; Select[Range[5500],psddQ] (* Harvey P. Dale, Oct 03 2012 *)