A261560 Semiprimes sp such that (sum of digits of (sp)) + (product of digits of (sp)) is also semiprime.

14, 33, 38, 39, 46, 49, 55, 69, 74, 82, 86, 93, 94, 111, 121, 122, 141, 142, 146, 161, 166, 202, 214, 221, 226, 247, 249, 254, 259, 262, 274, 278, 287, 295, 301, 303, 323, 334, 346, 386, 411, 427, 445, 454, 458, 469, 485, 489, 501, 505, 529, 542, 565, 586, 589

Offset: 1

Author

K. D. Bajpai, Aug 24 2015

Keywords

• nonn
• base

Examples

			a(1) = 14 = (2 * 7), is semiprime. (1+4) + (1*4) = 9 = (3 * 3) is also semiprime.
a(3) = 38 = (2 * 19), is semiprime. (3+8) + (3*8) = 35 = (7 * 5) is also semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A061762, A118688, A118689, A118690.

Programs

Magma

IsSemiprime:=func; [n: n in [11..300] | IsSemiprime(n) and IsSemiprime(k) where k is (&+Intseq(n) + &*Intseq(n))];

Maple

with(numtheory): select(n -> bigomega(n)=2 and bigomega( add(d, d=convert(n, base, 10)) + mul(d, d=convert(n, base, 10)) ) = 2, [seq(n, n=1..300)]);

Mathematica

Select[Range[2000], PrimeOmega[#] == 2 && PrimeOmega[(Plus @@ IntegerDigits[#]) + (Times @@ IntegerDigits[#])] == 2 &]

PARI

for(n = 1, 300, d = digits(n); pd = prod(i = 1, #d, d[i]); if(bigomega(n)==2 && bigomega(sumdigits(n) + pd)==2, print1(n,", ")));