A316190 a(n) is the distance between n and the nearest prime power (in the sense of A246655) other than n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3

Offset

1,11

References

S. M. Gonek, A formula of Landau and mean values of Zeta(s), Topics in Analytic Number Theory, ed. by S. W. Graham and J. D. Vaaler, 92-97, Univ. Texas Press 1985.

S. M. Gonek, An explicit formula of Landau and its applications to the theory of the zeta-function, Contemporary Math. 143 (1993), 395-413.

Links

Peter Luschny, Table of n, a(n) for n = 1..10000

E. Landau, Über die Nullstellen der Zetafunktion, Math. Annalen 71, 548-564, (1911).

Example

Note that 1369, 1373, 1381 and 1399 are prime powers. This leads to the mapping:
1373 -> 4,
1374 -> 1,
1375 -> 2,
1376 -> 3,
1377 -> 4,
1378 -> 3,
1379 -> 2,
1380 -> 1,
1381 -> 8.

Maple

A316190_list := proc(N) local a, b, d, m, k, P, R; R := NULL; m := 1;
P := select(t -> nops(numtheory:-factorset(t)) = 1 or t = 0, [$0..N]);
for k from 1 to nops(P)-1 do
    a := P[k]; b := P[k+1];
    if m = a then
       R := R, min(m - P[k-1] , b - m);
       m := m + 1;
    fi;
    while m < b do
        R := R, min(m - a , b - m);
        m := m + 1;
    od;
od; [R] end:
A316190_list(100);

Mathematica

a[n_] := Module[{k = 1}, While[!PrimePowerQ[n+k] && !PrimePowerQ[n-k], k++]; k]; Array[a, 100] (* Jean-François Alcover, Jul 25 2019 *)

Crossrefs

Cf. A246655, A316191.

Sequence in context: A111620 A111628 A161974 * A358236 A330738 A025921

Adjacent sequences: A316187 A316188 A316189 * A316191 A316192 A316193

Keyword

nonn

Author

Peter Luschny, Jun 26 2018

Status

approved