A137417 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value a(n).

1, 3, 3, 4, 8, 9, 7, 12, 9, 10, 11, 12, 21, 21, 24, 16, 17, 27, 19, 42, 21, 33, 23, 36, 25, 26, 27, 28, 29, 30, 31, 48, 33, 72, 56, 36, 37, 57, 63, 40, 41, 63, 43, 44, 72, 69, 47, 48, 49, 75, 51, 78, 53, 81, 88, 84, 57, 87, 59, 126, 61, 135, 63, 64, 65, 99, 67, 68, 69, 70, 71

Offset

1,2

Comments

At the vast majority of positions the term is changed at most once, but at some positions a change occurs twice. An example is position 20. In step 4 the term at position 4 + a(4) = 8 is changed to 8 + a(4) = 12; in step 8 the term at position 8 + a(8) = 20 is changed to 20 + a(8) = 32; in step 10 the term at position 10 + a(10) = 20 is changed to a(20) + a(10) = 32 + 10 = 42.

The first position where the term is changed three times is 3498. [Klaus Brockhaus, Apr 23 2008]

The first position where the term is changed four times is 1024914. [Rémy Sigrist, Mar 11 2017]

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of first 2000000 terms

Mathematica

Block[{a, nn = 71}, a = Range[Max[3, IntegerLength[nn]] nn]; Do[a[[n + a[[n]]]] = a[[n + a[[n]]]] + a[[n]], {n, nn}]; a[[1 ;; nn]] ] (* Michael De Vlieger, Jul 28 2021 *)

Crossrefs

Cf. A000027.

Sequence in context: A340429 A147679 A339054 * A137418 A357306 A285445

Adjacent sequences: A137414 A137415 A137416 * A137418 A137419 A137420

Keyword

easy,nonn

Author

Ctibor O. Zizka, Apr 16 2008

Extensions

Extended by Klaus Brockhaus, Apr 23 2008

Status

approved