A376311 - OEIS

A376311

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

1, 3, 6, 31, 150, 515, 13391, 131964, 664313, 5392318, 159468672, 134453711, 28728014494, 50131235121, 634347950217, 48136136076258, 1954623227727573, 14433681032814706, 76465679305346797

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

The sequence of squarefree numbers (A005117) is:

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

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

1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...

The positions of first appearances are a(n).

MATHEMATICA

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

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

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

CROSSREFS

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

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

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

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

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

A000040 lists the prime numbers, differences A001223.

A000961 and A246655 list prime-powers, differences A057820.

A003242 counts compressed compositions, ranks A333489.

A005117 lists squarefree numbers, differences A076259.

A013929 lists nonsquarefree numbers, differences A078147.

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

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

Sequence in context: A182274 A103091 A186940 * A101751 A374876 A274999

Adjacent sequences: A376308 A376309 A376310 * A376312 A376313 A376314

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 22 2024

EXTENSIONS

a(11)-a(19) from Amiram Eldar, Sep 24 2024

STATUS

approved