A306965 - 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