A377703 - OEIS

A377703

First differences of the sequence A345531(k) = least prime-power greater than the k-th prime.

1, 3, 1, 5, 3, 3, 4, 2, 6, 1, 9, 2, 4, 2, 10, 2, 3, 7, 2, 6, 2, 8, 8, 4, 2, 4, 2, 4, 8, 7, 9, 2, 10, 2, 6, 6, 4, 2, 10, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 2, 13, 7, 6, 2, 6, 4, 2, 6, 18, 4, 2, 4, 14, 6, 6, 6, 4, 6, 2, 12, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6

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OFFSET

1,2

COMMENTS

What is the union of this sequence? In particular, does it contain 17?

LINKS

Table of n, a(n) for n=1..83.

MATHEMATICA

Differences[Table[NestWhile[#+1&, Prime[n]+1, !PrimePowerQ[#]&], {n, 100}]]

PROG

(Python)

from sympy import factorint, prime, nextprime

def A377703(n): return -next(filter(lambda m:len(factorint(m))<=1, count((p:=prime(n))+1)))+next(filter(lambda m:len(factorint(m))<=1, count(nextprime(p)+1))) # Chai Wah Wu, Nov 14 2024

CROSSREFS

First differences of A345531.

A000961 lists the powers of primes, differences A057820.

A001597 lists the perfect-powers, differences A053289, seconds A376559.

A007916 lists the non-perfect-powers, differences A375706, seconds A376562.

A024619 lists the non-prime-powers, differences A375735, seconds A376599.

A080101 counts prime-powers between primes (exclusive).

A246655 lists the prime-powers, differences A057820 without first term.

A361102 lists the non-powers of primes, differences A375708.

A366833 counts prime-powers between primes, see A053607, A304521, A377057 (positive), A377286 (zero), A377287 (one), A377288 (two).

A377432 counts perfect-powers between primes, see A377434 (one), A377436 (zero), A377466 (multiple).

Cf. A000040, A008864, A031218, A377281, A377282, A377286, A377289, A377468.