

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
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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



