login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Position of first appearance of n in the sequence of first differences of squarefree numbers, or the sequence ends if there is none.
25

%I #11 Sep 24 2024 09:31:30

%S 1,3,6,31,150,515,13391,131964,664313,5392318,159468672,134453711,

%T 28728014494,50131235121,634347950217,48136136076258,1954623227727573,

%U 14433681032814706,76465679305346797

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

%e The sequence of squarefree numbers (A005117) is:

%e 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...

%e The sequence of first differences (A076259) of squarefree numbers is:

%e 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 The positions of first appearances are a(n).

%t mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];

%t q=Differences[Select[Range[10000],SquareFreeQ]];

%t Table[Position[q,k][[1,1]],{k,mnrm[q]}]

%Y This is the position of first appearance of n in A076259, ones A375927.

%Y For compression instead of positions of first appearances we have A376305.

%Y For run-lengths instead of first appearances we have A376306.

%Y For run-sums instead of first appearances we have A376307.

%Y For prime-powers instead of squarefree numbers we have A376341.

%Y A000040 lists the prime numbers, differences A001223.

%Y A000961 and A246655 list prime-powers, differences A057820.

%Y A003242 counts compressed compositions, ranks A333489.

%Y A005117 lists squarefree numbers, differences A076259.

%Y A013929 lists nonsquarefree numbers, differences A078147.

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

%Y Cf. A007674, A053797, A053806, A061398, A072284, A112925, A120992, A375707, A376312, A376342.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Sep 22 2024

%E a(11)-a(19) from _Amiram Eldar_, Sep 24 2024