A176651 - OEIS

%I #12 Feb 06 2019 03:49:07

%S 3,5,6,7,10,11,15,19,20,23,24,32,46,57,63,65,69,77,85,86,98,99,108,

%T 119,123,127,130,131,132,140,150,154,161,166,167,193,205,217,233,237,

%U 264,276,280,303,307,326,331,332,339,343,362,368,369,380,382,385,386,415

%N Numbers k such that both semiprime(k)/prime(j+1) and semiprime(k+1)/prime(j) are prime for some j.

%e 3 is a term because semiprime(3)/prime(1+1) = 6/3 = 2 (prime) and semiprime(3+1)/prime(1) = 10/2 = 5 (prime);

%e 5 is a term because semiprime(5)/prime(3+1) = 14/7 = 2 (prime) and semiprime(5+1)/prime(3) = 15/5 = 3 (prime).

%p isA176651 := proc(n) pfsn := convert(numtheory[factorset]( A001358(n) ),list) ; pfsn1 := convert(numtheory[factorset]( A001358(n+1) ),list) ; op(1,pfsn) = nextprime( op(1,pfsn1)) or op(1,pfsn) = nextprime( op(-1,pfsn1)) or op(-1,pfsn) = nextprime( op(1,pfsn1)) or op(-1,pfsn) = nextprime( op(-1,pfsn1)) ; end proc: for n from 1 to 600 do if isA176651(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Apr 26 2010

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 22 2010

%E Corrected (6 inserted) and extended beyond 132 by _R. J. Mathar_, Apr 26 2010