A375734 - OEIS

A375734

Indices of consecutive prime-powers (exclusive) differing by 1. Positions of 1's in A057820.

1, 2, 3, 5, 6, 10, 17, 43, 70, 1077, 6635, 12369, 43578, 105102700

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OFFSET

1,2

COMMENTS

The corresponding prime-powers A246655(a(n)) are given by A006549.

From A006549, it is not known whether this sequence is infinite.

LINKS

Table of n, a(n) for n=1..14.

FORMULA

Numbers k such that A246655(k+1) - A246655(k) = 1.

The inclusive version is a(n) + 1 shifted.

EXAMPLE

The fifth prime-power is 7 and the sixth is 8, so 5 is in the sequence.

MATHEMATICA

Join@@Position[Differences[Select[Range[100], PrimePowerQ]], 1]

CROSSREFS

For nonprime numbers (A002808) we have A375926, differences A373403.

Positions of 1's in A057820.

First differences are A373671.

For nonsquarefree numbers we have A375709, differences A373409.

For non-prime-powers we have A375713.

For non-perfect-powers we have A375740.

For squarefree numbers we have A375927, differences A373127.

Prime-powers:

- terms: A000961, complement A024619.

- differences: A057820.

- runs: A373675, A373673, A373674, A174965

- anti-runs: A373576, A120430, A006549, A373671

Non-prime-powers:

- terms: A361102

- differences: A375708

- runs: A373678, A373676, A373677, A110969 (A373669, sorted A373670).

- anti-runs: A373679, A373575, A255346, A373672

A000040 lists all of the primes, differences A001223.

A025528 counts prime-powers up to n.

Cf. A007916, A014963, A027833, A046933, A053289, A093555, A375714.

Sequence in context: A335597 A374427 A164523 * A227305 A326612 A240949

Adjacent sequences: A375731 A375732 A375733 * A375735 A375736 A375737

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 04 2024

EXTENSIONS

a(14) from Amiram Eldar, Sep 24 2024

STATUS

approved