A060253 Numbers n such that difference between n-th prime and n-th composite number is prime.

1, 2, 3, 4, 7, 9, 10, 11, 13, 14, 19, 24, 25, 32, 34, 37, 60, 64, 65, 67, 71, 75, 79, 83, 87, 95, 104, 105, 111, 115, 124, 130, 132, 133, 138, 145, 152, 153, 161, 163, 166, 174, 182, 187, 188, 190, 212, 213, 217, 220, 243, 246, 251, 255, 257, 264, 275, 279, 281

Offset: 1

Author

Robert G. Wilson v, Mar 22 2001

Keywords

• easy
• nonn

Examples

			n=10: p(10)=29, c(10)=18, c(10)-p(10)=11, so 10=a(7) is here.
		

Crossrefs

Numbers n such that A038529(n) is prime. Cf. A000040, A002808.

Programs

Mathematica

f[ n_Integer ] := Block[ {k = n + PrimePi[ n ] + 1}, While[ k - PrimePi[ k ] - 1 != n, k++ ]; k ]; Select[ Range[ 500 ], PrimeQ[ Prime[ # ] - f[ # ] ] & ]
Module[{nn=2000,pr,cm,len,th},pr=Prime[Range[PrimePi[nn]]];cm=Select[ Range[ nn],CompositeQ];len=Min[Length[pr],Length[cm]];th=Thread[{Take[ pr,len],Take[ cm,len]}];Position[th,?(PrimeQ[Abs[#[[1]]-#[[2]]]]&)]]// Quiet//Flatten (* _Harvey P. Dale, Jun 29 2020 *)

Formula

Values of n such that A000040(n)-A002808(n)=p(n)-c(n) is a prime number.