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

1,2

Links

Table of n, a(n) for n=1..59.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A047548 A095378 A141489 * A066276 A047340 A270711

Adjacent sequences: A060250 A060251 A060252 * A060254 A060255 A060256

Keyword

easy,nonn

Author

Robert G. Wilson v, Mar 22 2001

Status

approved