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A193594 Number of attractors under iteration of sum of cubes of digits in base b. 2
1, 6, 9, 6, 9, 34, 11, 28, 15, 46, 22, 50, 49, 60, 86, 86, 60, 128, 22, 58, 118, 93, 64, 185, 5, 109, 102, 100, 122, 184, 51, 94, 205, 131, 173, 275, 67, 216, 131, 127, 34, 360, 114, 78, 215, 213, 393, 479, 76, 254, 634, 197, 214, 496, 348, 170, 437, 349, 290 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

If b>=2 and a >= 2*b^3, then S(a,3,b)<a. For each positive integer a, there is a positive integer m such that S^m(a,3,b)<2*b^3. (Grundman/Teeple, 2001, Lemma 8 and Corollary 9.)

LINKS

Table of n, a(n) for n=2..60.

H. G. Grundman, E. A. Teeple, Generalized Happy Numbers, Fibonacci Quarterly 39 (2001), nr. 5, p. 462-466.

EXAMPLE

In the decimal system all integers go to (1); (153); (370); (371); (407) or (55, 250,133); (136, 244); (160, 217, 352); (919, 1459) under the iteration of sum of cubes of digits, hence there are five fixed points, two 2-cycles and two 3-cycles. Therefore a(10) = 5 + 2*2 + 2*3 = 15.

MAPLE

S:=proc(n, p, b) local Q, k, N, z; Q:=[convert(n, base, b)]; for k from 1 do N:=Q[k]; z:=convert(sum(N['i']^p, 'i'=1..nops(N)), base, b); if not member(z, Q) then Q:=[op(Q), z]; else Q:=[op(Q), z]; break; fi; od; return Q; end:

NumberOfAttractors:=proc(b) local A, i, Q; A:=[]: for i from 1 to 2*b^3 do Q:=S(i, 3, b); A:=[op(A), Q[nops(Q)]]; od: return(nops({op(A)})); end:

seq(NumberOfAttractors(b), b=2..20);

CROSSREFS

Cf. A193586.

Sequence in context: A118947 A023410 A010725 * A011480 A283743 A339764

Adjacent sequences:  A193591 A193592 A193593 * A193595 A193596 A193597

KEYWORD

nonn,base

AUTHOR

Martin Renner, Jul 31 2011

STATUS

approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)