A266998 Number of iterations of the map "n -> sum of the triangular numbers whose indices are the digits of n" needed to reach 1.

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

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: A004554 A178959 A370113 * A021609 A364966 A140684

Adjacent sequences: A266995 A266996 A266997 * A266999 A267000 A267001

Keyword

base,easy,nonn

Author

Ivan N. Ianakiev, Jan 09 2016

Status

approved