A087686 Elements of A004001 that repeat consecutively.

1, 2, 4, 7, 8, 12, 14, 15, 16, 21, 24, 26, 27, 29, 30, 31, 32, 38, 42, 45, 47, 48, 51, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 71, 76, 80, 83, 85, 86, 90, 93, 95, 96, 99, 101, 102, 104, 105, 106, 109, 111, 112, 114, 115, 116, 118, 119, 120, 121, 123, 124, 125, 126, 127

Offset: 1

Author

Roger L. Bagula, Sep 27 2003

Keywords

• nonn

Comments

Complement of A088359; A051135(a(n)) > 1. [Reinhard Zumkeller, Jun 03 2011]

From Antti Karttunen, Jan 18 2016: (Start)

This set of numbers is closed with respect to A004001, see A266188.

After 1, one more than the positions of zeros in A093879.

(End)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004001, A051135, A093879.

Cf. A088359 (complement), A188163 (almost complement).

Cf. A080677 (the least monotonic left inverse).

Cf. also A266188, A265901, A265903, A267110, A267111, A267112.

Programs

Haskell

import Data.List (findIndices)
a087686 n = a087686_list !! (n-1)
a087686_list = map succ $ findIndices (> 1) a051135_list
-- Reinhard Zumkeller, Jun 03 2011
(Scheme, with Antti Karttunen's IntSeq-library)
(define A087686 (MATCHING-POS 1 1 (lambda (n) (> (A051135 n) 1))))
;; Antti Karttunen, Jan 18 2016

Mathematica

Conway[n_Integer?Positive] := Conway[n] =Conway[Conway[n-1]] + Conway[n - Conway[n-1]] Conway[1] = Conway[2] = 1 digits=1000 a=Table[Conway[n], {n, 1, digits}]; b=Table[If[a[[n]]-a[[n-1]]==0, a[[n]], 0], {n, 2, digits}]; c=Delete[Union[b], 1]

Formula

Other identities. For all n >= 1:

A080677(a(n)) = n. [See comments in A080677.]