A193586 Number of attractors under iteration of sum of squares of digits in base n.

1, 5, 1, 6, 9, 13, 10, 8, 9, 9, 20, 13, 12, 35, 7, 15, 7, 21, 27, 37, 24, 36, 32, 26, 10, 36, 27, 28, 10, 56, 22, 26, 23, 63, 39, 27, 19, 67, 9, 36, 40, 54, 54, 48, 18, 73, 52, 75, 18, 117, 52, 74, 22, 65, 48, 53, 45, 44, 43, 18, 30, 67, 39, 49, 87, 111, 15

Offset: 2

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Comments

If b>=2 and a>=b^2 then S(a,2,b)

Examples

			In the decimal system all integers go to (1) or (4, 16, 37, 58, 89, 145, 42, 20) under the iteration of sum of squares of digits, hence there is one fixed point and one 8-cycle. Therefore a(10) = 1 + 8 = 9.
		

Links

• Martin Renner, Table of n, a(n) for n = 2..300
• H. G. Grundman, E. A. Teeple, Generalized Happy Numbers, Fibonacci Quarterly 39 (2001), nr. 5, p. 462-466.

Crossrefs

Cf. A193583, A193585.

Programs

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 b^2 do Q:=S(i,2,b); A:=[op(A),Q[nops(Q)]]; od: return(nops({op(A)})); end:
seq(NumberOfAttractors(b),b=2..50);

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