cp's OEIS Frontend

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

%I A376310 #7 Sep 23 2024 14:13:40
%S A376310 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,
%T A376310 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,
%U A376310 14,4,2,4,14,12,4,2,4,6,2,18,4,6,8,4,8,10,2
%N A376310 Run-sums of the sequence of first differences of prime-powers.
%e A376310 The sequence of prime-powers (A246655) is:
%e A376310   2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, ...
%e A376310 The sequence of first differences (A057820) of prime-powers is:
%e A376310   1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, ...
%e A376310 with runs:
%e A376310   (1,1,1),(2),(1,1),(2,2),(3),(1),(2),(4),(2,2,2,2),(1),(5),(4),(2),(4), ...
%e A376310 with sums A376310 (this sequence).
%t A376310 Total/@Split[Differences[Select[Range[100],PrimePowerQ]]]
%Y A376310 For primes instead of prime-powers we have A373822, halved A373823.
%Y A376310 For squarefree numbers instead of prime-powers we have A376307.
%Y A376310 For compression instead of run-sums we have A376308.
%Y A376310 For run-lengths instead of run-sums we have A376309.
%Y A376310 For positions of first appearances we have A376341, sorted A376340.
%Y A376310 A000040 lists the prime numbers, differences A001223.
%Y A376310 A000961 and A246655 list prime-powers, first differences A057820.
%Y A376310 A003242 counts compressed compositions, ranks A333489.
%Y A376310 A005117 lists squarefree numbers, differences A076259.
%Y A376310 A024619 and A361102 list non-prime-powers, first differences A375708.
%Y A376310 A116861 counts partitions by compressed sum, by compressed length A116608.
%Y A376310 A124767 counts runs in standard compositions, anti-runs A333381.
%Y A376310 A238130, A238279, A333755 count compositions by number of runs.
%Y A376310 A274174 counts contiguous compositions, ranks A374249.
%Y A376310 A373948 encodes compression using compositions in standard order.
%Y A376310 Cf. A001597, A006549, A007916, A025475, A037201, A053289, A054265, A110969, A120430, A174965, A251092, A375706.
%K A376310 nonn
%O A376310 1,1
%A A376310 _Gus Wiseman_, Sep 22 2024