A264668 -id:A264668 - cp's OEIS frontend

A061486 Let the number of digits in n be k; a(n) = sum of the products of the digits of n taken r at a time where r ranges from 1 to k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 1, 3

Offset: 0

Amarnath Murthy, May 06 2001

Differs from A264600 first at n=101: a(101) = 3 != A264600(101) = 12. - Alois P. Heinz, Nov 20 2015

			a(34) = 3 + 4 + 3*4 = 19, a(124) = (1+2+4)+(1*2+2*4+1*4)+(1*2*4) = 29.

Alois P. Heinz, Table of n, a(n) for n = 0..20000
Eric Weisstein's World of Mathematics, Symmetric polynomial.
Wikipedia, Elementary symmetric polynomial.

Cf. A264600, A264668.

with(combinat):
a:= n-> (l-> add(mul(l[i], i=w), w=choose(
         nops(l)))-1)(convert(n, base, 10)):
seq(a(n), n=0..101);  # Alois P. Heinz, Nov 20 2015

sympol(X, n)=my(s=0); forvec(i=vector(n, j, [1, #X]), s+=prod(k=1, n, X[i[k]]), 2); s ;
a(n) = my(d=digits(n)); sum(k=1, #d, sympol(d, k)); \\ Michel Marcus, Apr 06 2021

More terms from Erich Friedman, Jun 03 2001

a(0)=0 prepended by Alois P. Heinz, Nov 20 2015

A264600 Let S_n denote the list of decimal numbers 0 to n, written backwards (allowing leading zeros) and arranged in lexicographic order; a(n) = position where backwards-n appears, starting indexing at 0.

Original entry on oeis.org

Offset: 0

N. J. A. Sloane, Nov 20 2015

			S_0 = [0], so a(0)=0,
...
S_9 = [0,1,2,3,4,5,6,7,8,9], so a(9) = 9,
S_10 = [0,01,1,2,3,4,5,6,7,8,9], so a(10) = 1,
S_11 = [0,01,1,11,2,3,4,5,6,7,8,9], so a(11) = 3,
...
S_20 = [0,01,02,1,11,2,21,3,31,4,41,5,51,6,61,7,71,8,81,9,91], so a(20) = 2, and so on

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 10000 terms from Chai Wah Wu)

Decimal analog of A264596.

Has same beginning as A061486 but is ultimately different: see A264668.

a:= proc(n) option remember; `if`(n=0, 0,
      irem(n, 10, 'r')*(r+1)+a(r))
    end:
seq(a(n), n=0..101);  # Alois P. Heinz, Nov 20 2015

A264600[0]=0;A264600[n_]:=A264600[n]=Mod[n,10](Floor[n/10]+1)+A264600[Floor[n/10]];Array[A264600,100,0] (* Paolo Xausa, Nov 04 2023, after Alois P. Heinz *)

def A264600(n):
    return sorted(str(i)[::-1] for i in range(n+1)).index(str(n)[::-1]) # Chai Wah Wu, Nov 20 2015

a(0) = 0, a(10n+m) = a(n) + m*(n+1) for m in {0,...,9}. - Alois P. Heinz, Nov 20 2015

More terms from Alois P. Heinz, Nov 20 2015

cp's OEIS Frontend

A061486 Let the number of digits in n be k; a(n) = sum of the products of the digits of n taken r at a time where r ranges from 1 to k.

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