A376265 Position of first appearance of n in A376264 (run-sums of first differences of nonsquarefree numbers), or 0 if there are none.

2, 8, 3, 1, 6222, 14, 308540, 18

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Formula

A376264(a(n)) = n.

Example

The sequence of nonsquarefree numbers (A013929) is:
  4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ...
with first differences (A078147):
  4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ...
with runs:
  (4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ...
with sums (A376264):
  4, 1, 3, 4, 4, 4, 1, 2, 1, 16, 1, 3, 2, 6, 4, 3, 1, 8, 3, 1, 4, 1, 3, 4, 4, ...
with first appearances at (A376265):
  2, 8, 3, 1, 6222, 14, 308540, 18, ...

Mathematica

mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
q=Total/@Split[Differences[Select[Range[10000], !SquareFreeQ[#]&]]]//Most;
Table[Position[q, k][[1, 1]], {k, mnrm[q]}]

Crossrefs

This is the position of first appearance of n in A376264.

The sorted version is A376266.

For run-lengths instead of firsts of run-sums we have A376267.

For compression instead of firsts of run-sums we have A376312.

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 (ones A375927).

A013929 lists nonsquarefree numbers, differences A078147.

A333254 lists run-lengths of differences between consecutive primes.

A376305 gives run-compression of first differences of squarefree numbers.

A376307 gives run-sums of first differences of squarefree numbers.

Cf. A037201, A053797, A053806, A120992, A373198, A373413, A373822, A375707, A376306, A376310, A376311.

Sequence in context: A320972 A273692 A006085 * A021357 A214072 A016640

Adjacent sequences: A376262 A376263 A376264 * A376266 A376267 A376268

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2024

Status

approved