A061077 a(n) is the sum of the products of the digits of the first n odd numbers.

1, 4, 9, 16, 25, 26, 29, 34, 41, 50, 52, 58, 68, 82, 100, 103, 112, 127, 148, 175, 179, 191, 211, 239, 275, 280, 295, 320, 355, 400, 406, 424, 454, 496, 550, 557, 578, 613, 662, 725, 733, 757, 797, 853, 925, 934, 961, 1006, 1069, 1150, 1150, 1150, 1150

Offset

1,2

References

Amarnath Murthy, Smarandache friendly numbers and a few more sequences, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.

Links

Table of n, a(n) for n=1..53.

Luca Onnis, On the general Smarandache's sigma product of digits, arXiv:2203.07227 [math.GM], 2022.

Formula

a(n) = Sum_{k = 1..n} (product of the digits of 2k-1).

From Luca Onnis, Mar 20 2022: (Start)

a(5*10^n) = (25/44)*(45^(n+1)-1).

a(n) <= (25/44)*(45^(log(n/5)+1)-1) for all n.

a(n) ~ (5/4)*A061078(n) as n -> infinity. (End)

Example

a(7) = 1 + 3 + 5 + 7 + 9 + 1*1 + 1*3 = 29.

Mathematica

Accumulate[Times @@@ IntegerDigits[Range[1, 99, 2]]] (* Luca Onnis, Mar 20 2022 *)

Prog

(PARI) pd(n) = my(d = digits(n)); prod(i=1, #d, d[i]);
a(n) = sum(k=1, n, pd(2*k-1)); \\ Michel Marcus, Feb 01 2015
(PARI) a(n) = {m=digits(2*n - 1); p=1; d=#m; for(i=1, #m, if(m[i]==0, d=i-1; break));
(25/44) * (45^(#m-1)-1) + sum(i=1, #m-1, (prod(j=1, #m-i-1, m[j])) * (m[#m-i]) * (m[#m-i]-1) * (5^(i + 1) * 9^(i-1)) / 2)+prod(k=1, #m-1, m[k])*(((m[#m]+1)^2)/4)} \\ Luca Onnis, Mar 20 2022
(Python)
from math import prod
def A061077(n): return sum(prod(int(d) for d in str(2*i+1)) for i in range(n)) # Chai Wah Wu, Mar 21 2022

Crossrefs

Cf. A061076, A061078.

Sequence in context: A339857 A074373 A067115 * A292675 A254719 A266918

Adjacent sequences: A061074 A061075 A061076 * A061078 A061079 A061080

Keyword

nonn,base,easy

Author

Amarnath Murthy, Apr 14 2001

Extensions

More terms from Matthew Conroy, Apr 16 2001

Offset corrected by Charles R Greathouse IV, Feb 01 2015

Incorrect formula removed by Luca Onnis, Mar 20 2022

Status

approved