A290963 Primes p such that sum of digits of p^3 is semiprime.
3, 7, 29, 41, 53, 59, 71, 83, 89, 113, 131, 137, 149, 157, 167, 173, 179, 197, 199, 227, 233, 239, 251, 263, 269, 281, 293, 317, 347, 379, 401, 409, 419, 431, 457, 463, 467, 479, 491, 503, 509, 521, 569, 617, 619, 641, 643, 647, 661, 677, 691, 701, 733, 743, 757, 761, 769, 797, 823, 829, 859, 883, 911
Offset: 1
Examples
a(2) = 7 is prime: 7^3 = 343; 3 + 4 + 3 = 10 = 2*5 that is semiprime. a(3) = 29 is prime : 29^3 = 24389; 2 + 4 + 3 + 8 + 9 = 26 = 2*13 that is semiprime. a(5) = 53 is prime : 53^3 = 148877; 1 + 4 + 8 + 8 + 7 + 7 = 35 = 5*7 that is semiprime.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Maple
select(p -> isprime(p) and numtheory:-bigomega(convert(convert(p^3,base,10),`+`)) = 2, [seq(i,i=3..1000,2)]); # Robert Israel, Aug 15 2017
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Mathematica
Select[Prime[Range[500]], PrimeOmega[Plus @@ IntegerDigits[#^3]] == 2 &]
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PARI
lista(nn) = forprime(p=3, nn, if(bigomega(sumdigits(p^3)) == 2, print1(p, ", "))); \\ Altug Alkan, Aug 16 2017