A372437 (Least binary index of n) minus (least prime index of n).

1, -1, 2, -2, 1, -3, 3, -1, 1, -4, 2, -5, 1, -1, 4, -6, 1, -7, 2, -1, 1, -8, 3, -2, 1, -1, 2, -9, 1, -10, 5, -1, 1, -2, 2, -11, 1, -1, 3, -12, 1, -13, 2, -1, 1, -14, 4, -3, 1, -1, 2, -15, 1, -2, 3, -1, 1, -16, 2, -17, 1, -1, 6, -2, 1, -18, 2, -1, 1, -19, 3

Offset

2,3

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Is 0 the only integer not appearing in the data?

Links

Table of n, a(n) for n=2..72.

Formula

a(2n) = A001511(n).

a(2n + 1) = -A038802(n).

a(n) = A001511(n) - A055396(n).

Mathematica

bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Min[bix[n]]-Min[prix[n]], {n, 2, 100}]

Crossrefs

Positions of first appearances are A174090.

For sum instead of minimum we have A372428, zeros A372427.

For maximum instead of minimum we have A372442, zeros A372436.

For length instead of minimum we have A372441, zeros A071814.

A003963 gives product of prime indices.

A019565 gives Heinz number of binary indices, adjoint A048675.

A029837 gives greatest binary index, least A001511.

A048793 lists binary indices, length A000120, reverse A272020, sum A029931.

A061395 gives greatest prime index, least A055396.

A070939 gives length of binary expansion.

A112798 lists prime indices, length A001222, reverse A296150, sum A056239.

Cf. A000720, A014499, A061712, A243055, A304818, A355536, A359495, A359402, A372429-A372432, A372588-A372591.

Sequence in context: A103360 A267409 A104469 * A144112 A178568 A357814

Adjacent sequences: A372432 A372433 A372436 * A372438 A372439 A372440

Keyword

sign,base

Author

Gus Wiseman, May 06 2024

Status

approved