A376310 Run-sums of the sequence of first differences of prime-powers.

3, 2, 2, 4, 3, 1, 2, 4, 8, 1, 5, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 4, 2, 1, 3, 6, 2, 10, 2, 12, 4, 2, 4, 6, 2, 10, 2, 4, 2, 24, 4, 2, 4, 6, 4, 8, 5, 1, 12, 2, 6, 4, 2, 6, 4, 14, 4, 2, 4, 14, 12, 4, 2, 4, 6, 2, 18, 4, 6, 8, 4, 8, 10, 2

Offset

1,1

Links

Table of n, a(n) for n=1..84.

Example

The sequence of prime-powers (A246655) is:
  2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, ...
The sequence of first differences (A057820) of prime-powers is:
  1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, ...
with runs:
  (1,1,1),(2),(1,1),(2,2),(3),(1),(2),(4),(2,2,2,2),(1),(5),(4),(2),(4), ...
with sums A376310 (this sequence).

Mathematica

Total/@Split[Differences[Select[Range[100], PrimePowerQ]]]

Crossrefs

For primes instead of prime-powers we have A373822, halved A373823.

For squarefree numbers instead of prime-powers we have A376307.

For compression instead of run-sums we have A376308.

For run-lengths instead of run-sums we have A376309.

For positions of first appearances we have A376341, sorted A376340.

A000040 lists the prime numbers, differences A001223.

A000961 and A246655 list prime-powers, first differences A057820.

A003242 counts compressed compositions, ranks A333489.

A005117 lists squarefree numbers, differences A076259.

A024619 and A361102 list non-prime-powers, first differences A375708.

A116861 counts partitions by compressed sum, by compressed length A116608.

A124767 counts runs in standard compositions, anti-runs A333381.

A238130, A238279, A333755 count compositions by number of runs.

A274174 counts contiguous compositions, ranks A374249.

A373948 encodes compression using compositions in standard order.

Cf. A001597, A006549, A007916, A025475, A037201, A053289, A054265, A110969, A120430, A174965, A251092, A375706.

Sequence in context: A237612 A362465 A111739 * A372490 A182214 A339505

Adjacent sequences: A376307 A376308 A376309 * A376311 A376312 A376313

Keyword

nonn

Author

Gus Wiseman, Sep 22 2024

Status

approved