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