A297173 -id:A297173 - cp's OEIS frontend

A357138 Minimal run-length of the n-th composition in standard order; a(0) = 0.

0, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Gus Wiseman, Sep 18 2022

nonn

A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

			Composition 92 in standard order is (2,1,1,3), so a(92) = 1.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

See link for more sequences related to standard compositions.
The version for Heinz numbers of partitions is A051904, for parts A055396.
For parts instead of run-length we have A333768, maximal A333766.
The opposite (maximal) version is A357137.
For first instead of minimal we have A357180, last A357181.
Cf. A000120, A001511, A003754, A029931, A051903, A056239, A061395, A070939, A297173, A356844, A357136.

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Table[If[n==0,0,Min[Length/@Split[stc[n]]]],{n,0,100}]

A100573 Smallest difference between distinct prime divisors of n, or 0 if n is a prime power.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 5, 2, 0, 0, 1, 0, 3, 4, 9, 0, 1, 0, 11, 0, 5, 0, 1, 0, 0, 8, 15, 2, 1, 0, 17, 10, 3, 0, 1, 0, 9, 2, 21, 0, 1, 0, 3, 14, 11, 0, 1, 6, 5, 16, 27, 0, 1, 0, 29, 4, 0, 8, 1, 0, 15, 20, 2, 0, 1, 0, 35, 2, 17, 4, 1, 0, 3, 0, 39, 0, 1, 12, 41, 26, 9, 0, 1, 6, 21, 28, 45

Offset: 1

Leroy Quet, Jan 02 2005

nonn

			For 30 = 2*3*5, 2 and 3 are separated by only 1, so a(30) = 1.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. also A046665, A297173.

<Labos Elemer, Jan 05 2005 *)
Table[Min[Differences[Transpose[FactorInteger[n]][[1]]]],{n,100}]/.\[Infinity]->0 (* Harvey P. Dale, Jul 27 2015 *)

A100573(n) = if(omega(n)<=1,0,my(ps=factor(n)[,1]); vecmin(vector((#ps)-1,i,ps[i+1]-ps[i]))); \\ Antti Karttunen, Mar 03 2018

More terms from Labos Elemer, Jan 05 2005

cp's OEIS Frontend

A357138 Minimal run-length of the n-th composition in standard order; a(0) = 0.

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