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

Author

M. F. Hasler, May 12 2016

Keywords

• nonn
• base

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Hereditary Representation.

Crossrefs

Cf. A273004, A056004, A222112.

Programs

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

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