A145351 Prime-indexed composites k such that lpf(k) + gpf(k) is a prime.

6, 10, 20, 22, 30, 44, 54, 58, 66, 82, 96, 108, 120, 136, 142, 144, 204, 232, 324, 330, 340, 352, 384, 464, 492, 544, 596, 616, 704, 738, 750, 792, 870, 894, 918, 960, 990, 1062, 1234, 1312, 1318, 1326, 1498, 1534, 1540, 1566, 1576, 1632, 1694, 1700, 1722

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 04 2009

Keywords

• nonn

Examples

			6 is a term because it is the 2nd composite number, 6=2*3, and 2+3=5 is prime;
10 is a term because it is the 5th composite number, 10=2*5, and 2+5=7 is prime;
22 is a term because it is the 13th composite number, 22=2*11, and 2+11=13 is prime;
44 is a term because it is the 29th composite number, 44=2*2*11, and 2+11=13 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002808, A020639 (lpf), A006530 (gpf).

Programs

Maple

A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc:
A065858 := proc(n) A002808(ithprime(n)) ; end proc:
A145351 := proc(n) c := A065858(n) ; if isprime(A020639(c) + A006530(c)) then printf("%d,",c) ; end if; end proc:
seq(A145351(n),n=1..400) ; # R. J. Mathar, May 01 2010

Mathematica

pfiQ[n_]:=Module[{f=FactorInteger[n]},PrimeQ[f[[1,1]]+f[[-1,1]]]]; Module[ {nn=2000,c},c=Select[ Range[nn],CompositeQ];Select[ Table[ Take[c,{n}][[1]],{n,Prime[Range[PrimePi[Length[c]]]]}],pfiQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 18 2019 *)

Extensions

Corrected (inserted 20 from n=5, 30 from n=8, removed 200) and extended beyond 204 by R. J. Mathar, May 01 2010

Edited by Jon E. Schoenfield, Feb 07 2019