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
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.
Programs
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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))
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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