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A060848 Difference between a nontrivial prime power (A025475) and the next prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A264597 A112603 A097294 * A265271 A350499 A006020
KEYWORD
nonn
AUTHOR
Labos Elemer, May 03 2001
STATUS
approved

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Last modified May 18 14:55 EDT 2024. Contains 372640 sequences. (Running on oeis4.)