A154370 Numbers k such that gpf(composite(k)) - lpf(composite(k)) is prime.

5, 7, 8, 11, 16, 18, 19, 23, 25, 27, 28, 30, 34, 36, 39, 42, 43, 50, 53, 54, 56, 57, 60, 62, 65, 72, 74, 76, 82, 83, 89, 91, 93, 95, 98, 102, 105, 108, 111, 114, 115, 119, 122, 128, 132, 134, 138, 139, 143, 147, 151, 153, 159, 161, 163, 170, 175, 176, 178, 182, 187

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Composite(5) = 10 = 5*2 and 5 - 2 = 3 (prime), so 5 is a term;
composite(7) = 14 = 7*2 and 7 - 2 = 5 (prime), so 7 is a term;
composite(8) = 15 = 5*3 and 5 - 3 = 2 (prime), so 8 is a term;
composite(11) = 20 = 5*2*2 and 5 - 2 = 3 (prime), so 11 is a term.

Maple

A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
for n from 1 to 500 do if isprime( A006530(A002808(n)) - A020639(A002808(n)) ) then printf("%d, ", n ) ; end if; end do: # R. J. Mathar, May 05 2010

Mathematica

Flatten @ Position[Select[Range[1000], CompositeQ], c_Integer /; PrimeQ[Last[#] - First[#]& @ FactorInteger[c][[All, 1]]]] (* Jean-François Alcover, Jul 24 2020 *)

Crossrefs

Cf. A000040 (primes), A002808 (composites).

Cf. A006530 (gpf), A020639 (lpf).

Sequence in context: A082728 A359629 A285081 * A045251 A099497 A327960

Adjacent sequences: A154367 A154368 A154369 * A154371 A154372 A154373

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 08 2009

Extensions

Corrected (30 inserted, 43 inserted, 100 removed, ...) by R. J. Mathar, May 05 2010

Status

approved