A074332 Direction from n-th perfect power to closest prime (-1 if down, 1 if up, 0 if two primes are closest).

-1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, -1, -1, 1, 0, 1, -1, 1, 0, 1, -1, -1, 0, -1, 1, -1, 0, -1, 1, 1, -1, 0, -1, 1, -1, 1, -1, -1, 1, 1, 0, 1, 1, -1, 1, 1, -1, -1, -1, 0, 0, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 0, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, -1, -1, 1, 1, -1, 1, 1, 0, -1, -1, 1, -1, 1, 1, 0, -1, 1, -1, 1, 1, 1, -1

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Formula

Sign(n-th perfect power - closest prime) or 0 if two primes are closest.

Example

The 7th perfect power (A001597) is 27. The closest prime to 27 is 29. sign(27-29)=-1, so a(7)=-1. The 11th perfect power is 64. There is no single closest prime to 64, since two primes are closest, namely 61 and 67, so a(11)=0.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; pp = Select[ Range[10000], !PrimeQ[ # ] && Apply[ GCD, Last[ Transpose[FactorInteger[ # ]]]] > 1 & ]; Join[{-1}, Sign[ Table[ NextPrim[pp[[n]]] - pp[[n]], {n, 1, 124}] - Table[ pp[[n]] - PrevPrim[pp[[n]]], {n, 1, 124}]]]
ppcp[n_]:=Module[{a=NextPrime[n, -1], b=NextPrime[n]}, Which[n-a==b-n, 0, n-a < b-n, 1, True, -1]]; ppcp/@Join[{1}, Select[Range[8000], GCD@@FactorInteger[#][[All, 2]]>1&]] (* Harvey P. Dale, Aug 28 2018 *)

Crossrefs

Cf. A001597.

Sequence in context: A266112 A331990 A301849 * A152065 A267870 A267878

Adjacent sequences: A074329 A074330 A074331 * A074333 A074334 A074335

Keyword

sign

Author

Neil Fernandez, Oct 12 2002

Extensions

Edited by Robert G. Wilson v, Oct 13 2002

Status

approved