A080732 Smallest distance from n to a prime power (as defined in A246655).

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2

Offset

1,21

Comments

a(n)=min (abs(n-k) : where k runs through the prime powers)

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Mathematica

nn = 100; pp = Select[Range[2, Prime[1 + PrimePi[nn]]], Length[FactorInteger[#]] == 1 &]; Table[Min[Abs[n - pp]], {n, nn}] (* T. D. Noe, Mar 14 2012 *)

Crossrefs

Cf. A051699, A246547, A301295.

There are four different sequences which may legitimately be called "prime powers": A000961 (p^k, k >= 0), A246655 (p^k, k >= 1), A246547 (p^k, k >= 2), A025475 (p^k, k=0 and k >= 2). When you refer to "prime powers", be sure to specify which of these you mean. - N. J. A. Sloane, Mar 24 2018

Sequence in context: A346377 A338757 A080733 * A301295 A215036 A294448

Adjacent sequences: A080729 A080730 A080731 * A080733 A080734 A080735

Keyword

nonn

Author

Benoit Cloitre, Mar 08 2003

Status

approved