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A377281
Difference between the n-th prime and the next prime-power (exclusive).
8
1, 1, 2, 1, 2, 3, 2, 4, 2, 2, 1, 4, 2, 4, 2, 6, 2, 3, 4, 2, 6, 2, 6, 8, 4, 2, 4, 2, 4, 8, 1, 6, 2, 10, 2, 6, 6, 4, 2, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 2, 5, 6, 6, 2, 6, 4, 2, 6, 14, 4, 2, 4, 14, 6, 6, 2, 4, 6, 2, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6
OFFSET
1,3
FORMULA
a(n) = A000015(prime(n)) - prime(n).
a(n) = A345531(n) - prime(n).
a(n) = A377282(prime(n)).
EXAMPLE
The twelfth prime is 37, with next prime-power 41, so a(12) = 4.
MATHEMATICA
Table[NestWhile[#+1&, Prime[n]+1, !PrimePowerQ[#]&]-Prime[n], {n, 100}]
PROG
(Python)
from itertools import count
from sympy import prime, factorint
def A377281(n): return -(p:=prime(n))+next(filter(lambda m:len(factorint(m))<=1, count(p+1))) # Chai Wah Wu, Oct 25 2024
CROSSREFS
For prime instead of prime-power we have A001223.
For powers of two instead of primes we have A013597, A014210, A014234, A244508, A304521.
This is the restriction of A377282 to the prime numbers.
For previous instead of next prime-power we have A377289, restriction of A276781.
A000015 gives the least prime-power >= n.
A000040 lists the primes, differences A001223.
A000961 lists the powers of primes, differences A057820, complement A361102.
A031218 gives the greatest prime-power <= n.
A080101 counts prime-powers between primes (exclusive), cf. A377286, A377287, A377288.
A246655 lists the prime-powers not including 1.
Sequence in context: A147301 A108380 A361231 * A302098 A112779 A366631
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2024
STATUS
approved