A176706 Primes p such that the p-th semiprime divided by the sum of the digits of p is a prime.

2, 3, 7, 23, 131, 313, 353, 397, 887, 1307, 1439, 1783, 2003, 2027, 2069, 2111, 2593, 2777, 3541, 4111, 4201, 4889, 5653, 5897, 6421, 6823, 8353, 8447, 9721, 9749, 11159, 11483, 12011, 12073, 12251, 13313, 14323, 14431, 15083, 15131, 15887, 17029

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 24 2010

Keywords

• nonn
• base

Examples

			131 is a term because the 131st semiprime is 415, the sum of the digits of 131 is 5, and 415/5 = 83, which is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001358, A007605, A106350.

Programs

Maple

isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
A001358 := proc(n) option remember ; if n = 1 then return 4 ; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do; end if; end proc:
A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc:
isA176706 := proc(n) if isprime(n) then r := A001358(n)/A007953(n) ; if type(r,'integer') then isprime(r) ; else false; end if; else false; end if; end proc:
for n from 1 to 2000 do p := ithprime(n) ; if isA176706(p) then printf("%d,",p) ; end if; end do: # R. J. Mathar, Apr 24 2010

Mathematica

Module[{semis=Select[Range[100000],PrimeOmega[#]==2&]},Select[ Prime[ Range[ PrimePi[ Length[semis]]]], PrimeQ[semis[[#]]/ Total[ IntegerDigits[ #]]]&]] (* Harvey P. Dale, May 10 2014 *)

Extensions

Keyword:base added, sequence extended by R. J. Mathar, Apr 24 2010