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 A316190 a(n) is the distance between n and the nearest prime power (in the sense of A246655) other than n. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A330738 A025921 A300978 Adjacent sequences:  A316187 A316188 A316189 * A316191 A316192 A316193 KEYWORD nonn AUTHOR Peter Luschny, Jun 26 2018 STATUS approved

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Last modified May 17 13:21 EDT 2022. Contains 353746 sequences. (Running on oeis4.)