login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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