A306965 If the decimal expansion of n is d_1 ... d_k, a(n) = Sum binomial(10,d_i).

1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 11, 20, 55, 130, 220, 262, 220, 130, 55, 20, 46, 55, 90, 165, 255, 297, 255, 165, 90, 55, 121, 130, 165, 240, 330, 372, 330, 240, 165, 130, 211, 220, 255, 330, 420, 462, 420, 330, 255, 220, 253, 262, 297, 372, 462

Offset

0,2

Comments

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.

References

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).

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.

H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.c.

Mathematica

a[n_] := Total[Binomial[10, #] & /@ IntegerDigits[n]]; Array[a, 55, 0] (* Amiram Eldar, Mar 07 2023 *)

Prog

(PARI) a(n) = my(d=digits(n)); sum(k=1, #d, binomial(10, d[k])); \\ Michel Marcus, Mar 07 2023

Crossrefs

Cf. A306958.

Sequence in context: A009540 A010926 A229395 * A045852 A226450 A105938

Adjacent sequences: A306962 A306963 A306964 * A306966 A306967 A306968

Keyword

nonn,base

Author

N. J. A. Sloane, Mar 18 2019

Status

approved