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A376340 Sorted positions of first appearances in A057820, the sequence of first differences of prime-powers.

%I A376340 #9 Sep 23 2024 22:43:04
%S A376340 1,4,9,12,18,24,34,47,60,79,117,178,198,206,215,244,311,402,465,614,
%T A376340 782,1078,1109,1234,1890,1939,1961,2256,2290,3149,3377,3460,3502,3722,
%U A376340 3871,4604,4694,6634,8073,8131,8793,12370,12661,14482,14990,15912,17140,19166
%N A376340 Sorted positions of first appearances in A057820, the sequence of first differences of prime-powers.
%e A376340 The terms together with their prime indices begin:
%e A376340      1: {}
%e A376340      4: {1,1}
%e A376340      9: {2,2}
%e A376340     12: {1,1,2}
%e A376340     18: {1,2,2}
%e A376340     24: {1,1,1,2}
%e A376340     34: {1,7}
%e A376340     47: {15}
%e A376340     60: {1,1,2,3}
%e A376340     79: {22}
%e A376340    117: {2,2,6}
%e A376340    178: {1,24}
%e A376340    198: {1,2,2,5}
%e A376340    206: {1,27}
%e A376340    215: {3,14}
%e A376340    244: {1,1,18}
%t A376340 q=Differences[Select[Range[100],PrimePowerQ]];
%t A376340 Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&]
%Y A376340 For compression instead of sorted firsts we have A376308.
%Y A376340 For run-lengths instead of sorted firsts we have A376309.
%Y A376340 For run-sums instead of sorted firsts we have A376310.
%Y A376340 The version for squarefree numbers is the unsorted version of A376311.
%Y A376340 The unsorted version is A376341.
%Y A376340 A000040 lists the prime numbers, differences A001223.
%Y A376340 A000961 and A246655 list prime-powers, first differences A057820.
%Y A376340 A003242 counts compressed compositions, ranks A333489.
%Y A376340 A005117 lists squarefree numbers, differences A076259.
%Y A376340 A024619 and A361102 list non-prime-powers, first differences A375708.
%Y A376340 A116861 counts partitions by compressed sum, by compressed length A116608.
%Y A376340 Cf. A001597, A006549, A007916, A025475, A037201, A053289, A078147, A110969, A120430, A174965, A373948, A375706.
%K A376340 nonn
%O A376340 1,2
%A A376340 _Gus Wiseman_, Sep 22 2024