A059734 Carryless 11^n base 10; a(n) is carryless sum of 10*a(n-1) and a(n-1).

1, 11, 121, 1331, 14641, 150051, 1650561, 17155171, 188606881, 1964664691, 10500200501, 115502205511, 1260524250621, 13865766756831, 141412323214141, 1555535555355551, 16000880008800061, 176008680086800671

Offset: 0

Author

Henry Bottomley, Feb 20 2001

Keywords

• base
• nonn

Comments

Subsequence of A002113. - Chai Wah Wu, Jul 30 2025

Examples

			a(7)=17155171 since a(6)=1650561 and digits of a(7) are sum mod 10 of 1, 6+1=7, 5+6=1, 0+5=5, 5+0=5, 6+5=1, 1+6=7 and 1.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..999
• David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version

Crossrefs

Cf. A004520, A006940, A008975, A361351, A002113.

Programs

Mathematica

Table[Sum[Mod[Binomial[n, m], 10]*10^m, {m, 0, n}], {n, 0, 30}] (* Roger L. Bagula and Gary W. Adamson, Sep 14 2008 *)

PARI

a(n) = fromdigits(Vec(Pol(digits(11))^n)%10); \\ Seiichi Manyama, Mar 10 2023

Python

from math import comb, prod
from sympy.ntheory.modular import crt
from gmpy2 import digits
def A059734(n):
    k, l = 0, len(s:=digits(n,5))
    for m in range(n+1):
        t = digits(m,5).zfill(l)
        k = 10*k+crt([5,2],[prod(comb(int(s[i]),int(t[i]))%5 for i in range(l))%5,int(not ~n & m)])[0]
    return k # Chai Wah Wu, Jul 30 2025

Formula

a(n)=Sum[Mod[Binomial[n, m], 10]*10^m, {m, 0, n}]. - Roger L. Bagula and Gary W. Adamson, Sep 14 2008