A060848 Difference between a nontrivial prime power (A025475) and the next prime.

1, 3, 2, 1, 4, 2, 5, 4, 3, 2, 6, 2, 3, 4, 8, 1, 4, 4, 6, 9, 12, 6, 4, 12, 6, 7, 30, 4, 12, 12, 5, 16, 6, 4, 10, 10, 12, 10, 6, 3, 4, 6, 10, 4, 6, 2, 4, 10, 6, 17, 4, 10, 4, 18, 6, 30, 12, 12, 4, 10, 27, 4, 6, 4, 12, 4, 28, 6, 2, 10, 4, 4, 10, 12, 18, 10, 10, 3, 12, 4, 12, 6, 10, 10, 18, 10, 12

Offset

1,2

Comments

a(n)=1 only for some powers of 2 corresponding to Fermat primes > 3. - Edited by Robert Israel, Jun 03 2021

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = nextprime(A025475(n)) - A025475(n) = A013632(A025475(n)).

Example

78125=5^7 is followed by 78137, the difference is 12.

Maple

N:= 10^5: # for prime powers <= N
S:= {}:
p:= 1:
do
  p:= nextprime(p);
  if p^2 > N then break fi;
  S:= S union {seq(p^i, i=2..floor(log[p](N)))}
od:
map(t -> nextprime(t)-t, sort(convert(S, list))); # Robert Israel, Jun 03 2021

Mathematica

NextPrime[#]-#&/@Select[Range[100000], PrimePowerQ[#]&&!PrimeQ[#]&] (* Harvey P. Dale, Oct 19 2022 *)

Crossrefs

Cf. A025475, A007918, A013632.

Sequence in context: A264597 A112603 A097294 * A265271 A350499 A006020

Adjacent sequences: A060845 A060846 A060847 * A060849 A060850 A060851

Keyword

nonn

Author

Labos Elemer, May 03 2001

Status

approved