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

Author

Labos Elemer, May 03 2001

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A025475, A007918, A013632.

Programs

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 *)

Formula

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