cp's OEIS Frontend

A376311 Position of first appearance of n in the sequence of first differences of squarefree numbers, or the sequence ends if there is none.

%I A376311 #11 Sep 24 2024 09:31:30
%S A376311 1,3,6,31,150,515,13391,131964,664313,5392318,159468672,134453711,
%T A376311 28728014494,50131235121,634347950217,48136136076258,1954623227727573,
%U A376311 14433681032814706,76465679305346797
%N A376311 Position of first appearance of n in the sequence of first differences of squarefree numbers, or the sequence ends if there is none.
%e A376311 The sequence of squarefree numbers (A005117) is:
%e A376311   1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...
%e A376311 The sequence of first differences (A076259) of squarefree numbers is:
%e A376311   1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...
%e A376311 The positions of first appearances are a(n).
%t A376311 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A376311 q=Differences[Select[Range[10000],SquareFreeQ]];
%t A376311 Table[Position[q,k][[1,1]],{k,mnrm[q]}]
%Y A376311 This is the position of first appearance of n in A076259, ones A375927.
%Y A376311 For compression instead of positions of first appearances we have A376305.
%Y A376311 For run-lengths instead of first appearances we have A376306.
%Y A376311 For run-sums instead of first appearances we have A376307.
%Y A376311 For prime-powers instead of squarefree numbers we have A376341.
%Y A376311 A000040 lists the prime numbers, differences A001223.
%Y A376311 A000961 and A246655 list prime-powers, differences A057820.
%Y A376311 A003242 counts compressed compositions, ranks A333489.
%Y A376311 A005117 lists squarefree numbers, differences A076259.
%Y A376311 A013929 lists nonsquarefree numbers, differences A078147.
%Y A376311 A116861 counts partitions by compressed sum, by compressed length A116608.
%Y A376311 Cf. A007674, A053797, A053806, A061398, A072284, A112925, A120992, A375707, A376312, A376342.
%K A376311 nonn,more
%O A376311 1,2
%A A376311 _Gus Wiseman_, Sep 22 2024
%E A376311 a(11)-a(19) from _Amiram Eldar_, Sep 24 2024