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A266998 Number of iterations of the map "n -> sum of the triangular numbers whose indices are the digits of n" needed to reach 1. 2
0, 6, 5, 2, 8, 4, 10, 14, 12, 1, 7, 3, 11, 8, 7, 6, 15, 9, 13, 6, 3, 5, 13, 12, 10, 13, 12, 9, 14, 5, 11, 13, 4, 7, 4, 13, 8, 13, 8, 2, 8, 12, 7, 7, 11, 12, 14, 13, 7, 8, 7, 10, 4, 11, 6, 14, 8, 8, 5, 4, 6, 13, 13, 12, 14, 13, 8, 9, 14, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: 1 is reachable for every n. Verified for n up to 10^6. - Ivan N. Ianakiev, Jan 10 2016

Proof: For every n > 59, A267238(n) < n. - Ivan N. Ianakiev, Jan 15 2016

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

6 iterations are needed to start from 2 and reach 1 (2->3->6->21->4->10->1), therefore a(2) = 6.

MATHEMATICA

f[n_] := Total[IntegerDigits[n] * (IntegerDigits[n] + 1)/2];

g[n_] := NestWhileList[f[#] &, n, # > 1 &]; h[n_] := Length[g[n]] - 1;

h/@Range@100

PROG

(PARI) strd(n) = {my(d = digits(n)); sum(k=1, #d, d[k]*(d[k]+1)/2); }

a(n) = {my(nb=0); while(n != 1, n = strd(n); nb++; ); nb; } \\ Michel Marcus, Jan 12 2016

CROSSREFS

Cf. A007770, A266999, A267238 (the underlying map).

Sequence in context: A198107 A004554 A178959 * A021609 A140684 A245632

Adjacent sequences:  A266995 A266996 A266997 * A266999 A267000 A267001

KEYWORD

base,easy,nonn

AUTHOR

Ivan N. Ianakiev, Jan 09 2016

STATUS

approved

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Last modified December 13 17:37 EST 2019. Contains 329970 sequences. (Running on oeis4.)