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

1,1

Links

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

Example

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.

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 &]

Prog

(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, ", ")));
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [11..300] | IsSemiprime(n) and IsSemiprime(k) where k is (&+Intseq(n) + &*Intseq(n))];

Crossrefs

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

Sequence in context: A225420 A107484 A076329 * A250186 A191676 A191866

Adjacent sequences: A261557 A261558 A261559 * A261561 A261562 A261563

Keyword

nonn,base

Author

K. D. Bajpai, Aug 24 2015

Status

approved