A084995 Numbers which can be written as the product of two different primes and the sum of digits is also prime.

14, 21, 34, 38, 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, 298, 302, 319, 326, 335, 346, 355, 362, 371, 377, 382, 386, 391, 395, 403, 407, 427, 445, 454, 458, 469, 478, 481, 485

Offset: 1

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 30 2003

Keywords

• nonn
• base

Examples

			E.g., 14 = 7*2 and 1+4 = 5 is also prime.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006881, A028834, A108606.

Programs

Mathematica

Module[{nn=60},Select[Union[Times@@@Subsets[Prime[Range[nn]],{2}]],PrimeQ[ Total[ IntegerDigits[#]]]&&#<=2Prime[nn]&]] (* Harvey P. Dale, Feb 28 2022 *)

PARI

is(n)={bigomega(n)==2 && !issquare(n) && isprime(sumdigits(n))}
select(is, [1..500]) \\ Andrew Howroyd, Jan 05 2020

Formula

Intersection of A028834 and A006881. - Andrew Howroyd, Jan 05 2020

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 05 2020