A074038 If n is the k-th single (i.e., non-twin) prime then a(n) = k, otherwise a(n) = 0.

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Aug 13 2002

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A007510, A049084, A074039.

Programs

Mathematica

upto = 100;
A074038list[upto_] := Module[{k = 0, v = Table[0, {upto}], n},
    For[n = 1, n <= upto, n++, If[PrimeQ[n] && (2 == n ||
    ((!PrimeQ[n-2]) && (!PrimeQ[n+2]))), k++; v[[n]] = k,
    v[[n]] = 0]]; v];
v074038 = A074038list[upto];
a[n_] := v074038[[n]];
Table[a[n], {n, 1, upto}] (* Jean-François Alcover, Dec 03 2021, after PARI code *)

PARI

up_to = 65537;
A074038list(up_to) = { my(k=0,v=vector(up_to)); for(n=1,up_to,if(isprime(n)&&(2==n||((!isprime(n-2))&&(!isprime(n+2)))),k++;v[n]=k, v[n] = 0)); (v); };
v074038 = A074038list(up_to);
A074038(n) = v074038[n];

Formula

A007510(a(n)) = n.