A176651 Numbers k such that both semiprime(k)/prime(j+1) and semiprime(k+1)/prime(j) are prime for some j.

3, 5, 6, 7, 10, 11, 15, 19, 20, 23, 24, 32, 46, 57, 63, 65, 69, 77, 85, 86, 98, 99, 108, 119, 123, 127, 130, 131, 132, 140, 150, 154, 161, 166, 167, 193, 205, 217, 233, 237, 264, 276, 280, 303, 307, 326, 331, 332, 339, 343, 362, 368, 369, 380, 382, 385, 386, 415

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Example

3 is a term because semiprime(3)/prime(1+1) = 6/3 = 2 (prime) and semiprime(3+1)/prime(1) = 10/2 = 5 (prime);
5 is a term because semiprime(5)/prime(3+1) = 14/7 = 2 (prime) and semiprime(5+1)/prime(3) = 15/5 = 3 (prime).

Maple

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

Crossrefs

Sequence in context: A157201 A067351 A067350 * A359879 A028762 A047328

Adjacent sequences: A176648 A176649 A176650 * A176652 A176653 A176654

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 22 2010

Extensions

Corrected (6 inserted) and extended beyond 132 by R. J. Mathar, Apr 26 2010

Status

approved