A081828 -id:A081828

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A081827

Successive differences of Hofstadter Q-sequence.

+10
7

0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, -1, 1, 1, 0, 1, 0, 0, 0, 4, -2, 0, 2, 0, 0, 0, 4, -3, 0, 3, 1, -2, 1, 2, -1, 1, 1, 0, 1, 0, 0, 0, 0, 8, -8, 1, 5, -2, -2, 4, 0, -2, 4, -2, 2, 0, 0, 0, 8, -7, -2, 7, -3, -2, 6, 1, -3, 1, 2, -1, 1, -1, 3, -2, 1, 2, 1, -1, 0, 3, -2, 1, 2, 0, -1, 2, 0, 0, 0, 0, 0, 16, -23, 11, 2, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,11

COMMENTS

a(A081829(n))<0; a(A081828(n))=0; a(A081830(n))>0; a(A194626(n))=1. [Reinhard Zumkeller, Sep 15 2011]

LINKS

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

Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence

Wikipedia, Hofstadter sequence

Index entries for Hofstadter-type sequences

FORMULA

a(n)=A005185(n+1)-A005185(n).

PROG

(Haskell)

a081827 n = a081827_list !! (n-1)

a081827_list = zipWith (-) (tail a005185_list) a005185_list

b081827 = bFile "A081827" a081827_list 1 10000 -- (0.34 secs)

-- Reinhard Zumkeller, Sep 15 2011

KEYWORD

sign,look

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

A081829

Numbers n such that the n-th term of Hofstadter Q-sequence is > (n+1)-th term.

+10
5

15, 24, 31, 35, 38, 48, 51, 52, 55, 57, 63, 64, 66, 67, 70, 73, 75, 77, 81, 84, 88, 96, 100, 103, 105, 109, 112, 115, 118, 119, 121, 124, 126, 127, 128, 130, 135, 138, 140, 141, 143, 144, 147, 149, 150, 152, 155, 158, 160, 162, 165, 168, 169, 171, 172, 174, 179

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A005185(a(n)+1) < A005185(a(n)); A081827(a(n)) < 0.

LINKS

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

Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence

Wikipedia, Hofstadter sequence

Index entries for Hofstadter-type sequences

FORMULA

Conjecture : a(n)/n>2 and a(n)/n->2

PROG

(Haskell)

import Data.List (findIndices)

a08182 n = a081829_list !! (n-1)

a081829_list = map (+ 1) $ findIndices (< 0) a081827_list

-- Reinhard Zumkeller, Sep 15 2011

CROSSREFS

Cf. A081828, A081830, A194626.

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

A081830

Numbers n such that the n-th term of Hofstadter Q-sequence is < (n+1)-th term.

+10
5

2, 3, 5, 6, 8, 11, 14, 16, 17, 19, 23, 26, 30, 33, 34, 36, 37, 39, 40, 42, 47, 49, 50, 53, 56, 58, 62, 65, 68, 69, 71, 72, 74, 76, 78, 79, 80, 83, 85, 86, 89, 95, 97, 98, 99, 101, 104, 106, 107, 108, 110, 113, 114, 116, 117, 120, 122, 123, 125, 129, 131, 132, 134, 136

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A005185(a(n)+1) > A005185(a(n)); A081827(a(n)) > 0.

LINKS

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

Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence

Wikipedia, Hofstadter sequence

Index entries for Hofstadter-type sequences

FORMULA

Conjecture : a(n)/n -> 2. a(n)=2n for n=2, 14, 16, 802, 804, 806, 810, 814, 824, 826, 832, 1116, 1120, 1124, 1126, 1130, 1172, 1178, 1228, 1230, 1254, 1258, 1298...

PROG

(Haskell)

import Data.List (findIndices)

a081830 n = a081830_list !! (n-1)

a081830_list = map (+ 1) $ findIndices (> 0) a081827_list

-- Reinhard Zumkeller, Sep 15 2011

CROSSREFS

Cf. A081828, A081829, A194626.

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

A194626

Numbers n such that next term of Hofstadter's Q-sequence differs by 1.

+10
5

2, 3, 5, 6, 8, 16, 17, 19, 34, 36, 39, 40, 42, 49, 69, 71, 74, 78, 80, 85, 132, 167, 175, 176, 180, 181, 225, 238, 261, 271, 320, 331, 338, 340, 341, 353, 365, 371, 507, 689, 690, 706, 721, 738, 746, 921, 932, 952, 990, 1012, 1046, 1212, 1351, 1352, 1373

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A005185(a(n)+1) = A005185(a(n)) + 1; A081827(a(n)) = 1.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence

Wikipedia, Hofstadter sequence

Index entries for Hofstadter-type sequences

PROG

(Haskell)