Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Nov 29 2023 13:27:29
%S 1,10,45,120,210,252,210,120,45,10,11,20,55,130,220,262,220,130,55,20,
%T 46,55,90,165,255,297,255,165,90,55,121,130,165,240,330,372,330,240,
%U 165,130,211,220,255,330,420,462,420,330,255,220,253,262,297,372,462
%N If the decimal expansion of n is d_1 ... d_k, a(n) = Sum binomial(10,d_i).
%C Kiss found all the finite cycles under iteration of this map. There is one fixed point, 505, and one cycle of length 2, (463, 540), and that's all.
%D P. Kiss, A generalization of a problem in number theory, Math. Sem. Notes Kobe Univ., 5 (1977), no. 3, 313-317. MR 0472667 (57 #12362).
%H Amiram Eldar, <a href="/A306965/b306965.txt">Table of n, a(n) for n = 0..10000</a>
%H P. Kiss, <a href="http://real-j.mtak.hu/9373/1/MTA_MatematikaiLapok_1974.pdf">A generalization of a problem in number theory</a>, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.
%H H. J. J. te Riele, <a href="https://ir.cwi.nl/pub/6662">Iteration of number-theoretic functions</a>, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.c.
%t a[n_] := Total[Binomial[10, #] & /@ IntegerDigits[n]]; Array[a, 55, 0] (* _Amiram Eldar_, Mar 07 2023 *)
%o (PARI) a(n) = my(d=digits(n)); sum(k=1, #d, binomial(10, d[k])); \\ _Michel Marcus_, Mar 07 2023
%Y Cf. A306958.
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_, Mar 18 2019