A230422 Positions of ones in A230410.

1, 8, 14, 16, 18, 22, 33, 35, 37, 41, 45, 51, 53, 57, 61, 71, 75, 82, 87, 96, 106, 116, 118, 120, 124, 128, 134, 136, 140, 144, 154, 158, 165, 170, 179, 189, 198, 200, 206, 208, 212, 216, 226, 230, 237, 242, 251, 261, 270, 272, 280, 289, 293, 300, 305, 314, 324

Offset

1,2

Comments

This sequence gives all n at which positions the successive terms A219666(n-1) & A219666(n) in the infinite trunk of the factorial beanstalk differ only in one digit position in their factorial base representations (A007623).

Please see further comments and examples in A230410.

Links

Antti Karttunen, Table of n, a(n) for n = 1..17517

Formula

For all n, A230406(a(n)) is one of the terms of A051683.

Example

14 is included, because A219666(13) = 40 = '1220' in factorial base representation, while A219666(14) = 46 = '1320' in factorial base, and they differ only by their third least significant digit.
16 is included, because A219666(15) = 48 = '2000' in factorial base representation, while A219666(16) = 52 = '2020' in factorial base, and they differ only by their second least significant digit.

Mathematica

nn = 10^4; m = 1; While[m! < Floor[6 nn/5], m++]; m; f[n_] := IntegerDigits[n, MixedRadix[Reverse@ Range[2, m]]]; Position[#, 1] &[Function[w, Count[Subtract @@ Map[PadLeft[#, Max@ Map[Length, w]] &, w], k_ /; k != 0]]@ Map[f@ # &, {#1, #2}] & @@@ Partition[#, 2, 1] &@ TakeWhile[Reverse@ NestWhileList[# - Total@ f@ # &, Floor[6 nn/5], # > 0 &], # <= nn &]] // Flatten (* Michael De Vlieger, Jun 27 2016, Version 10.2 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A230422 (MATCHING-POS 1 1 (lambda (i) (= 1 (A230410 i)))))

Crossrefs

Subset: A231718. Cf. also A230410 and A258010 (first differences).

Sequence in context: A103338 A250004 A114456 * A050681 A292867 A235143

Adjacent sequences: A230419 A230420 A230421 * A230423 A230424 A230425

Keyword

nonn

Author

Antti Karttunen, Nov 10 2013

Status

approved