A273005 Sum of coefficients in the hereditary representation of n in base 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 3

Offset

0,3

Links

Table of n, a(n) for n=0..100.

Eric Weisstein's World of Mathematics, Hereditary Representation.

Formula

If n = Sum_{j=1..k} d_j*10^(e_j) where 0 <= e_1 < ... < e_k and 1 <= d_j <= 9, then a(n) = Sum_{j=1..k} (d_j + a(e_j)). - Pontus von Brömssen, Sep 17 2020

Example

266 = 6 + 6*10^1 + 2*10^2 which can be represented as [6, [6, [1]], [2, [2]]], therefore a(266) = 6 + 6 + 1 + 2 + 2 = 17.

Prog

(PARI) (hr(n, b=10)=if(1<#n=digits(n, b), my(v=if(n[#n], [n[#n]], [])); forstep(i=#n-1, 1, -1, n[i]&&v=concat(v, [[n[i], hr(#n-i, b)]])); v, n)); (cc(v)=if(type(v)=="t_VEC", sum(i=1, #v, cc(v[i])), v)); a(n)=cc(hr(n, 10))
(Python)
def A273005(n):
  s=str(n)[::-1]
  return sum(int(s[i])+A273005(i) for i in range(len(s)) if s[i]!='0') # Pontus von Brömssen, Sep 17 2020

Crossrefs

Cf. A273004, A056004, A222112.

Sequence in context: A276716 A189506 A173529 * A093017 A156230 A028897

Adjacent sequences: A273002 A273003 A273004 * A273006 A273007 A273008

Keyword

nonn,base

Author

M. F. Hasler, May 12 2016

Status

approved