A272233 Number of steps before n1(i) = n2(i) when n1(i) = n1(i-1) + digsum(n2(i-1)), n2(i) = n2(i-1) + digsum(n1(i-1)) and n1(1) = 10^(n-1), n2(1) = 0.

1, 12, 57, 22820, 754504

Offset: 0

Author

Anthony Sand, Apr 23 2016

Keywords

• nonn
• base
• more

Comments

The sequence takes two different numbers, n1 and n2, and simultaneously adds the digit sum of n1 to n2 and the digit sum of n2 to n1. This process continues until n1 = n2. The two numbers are initialized with n1 = 10^(n-1) and n2 = 0.

a(5) > 10^12. - Lars Blomberg, Jul 19 2017

Examples

			10 > 0, 10 > 1, 11 > 2, 13 > 4, 17 > 8, 25 > 16, 32 > 23, 37 > 28, 47 > 38, 58 > 49, 71 > 62, 79 > 70, 86 = 86
		

Crossrefs

Cf. A004207, A272235

Programs

PARI

{digsum(num) = d=digits(num,b); return(sum(i=1,#d,d[i]));} {doubledigsum() = b=10; nmx=5; for(n=1,nmx, n1=b^(a-1); n2=0; c=0; until(n1==n2, s1=digsum(n1); s2=digsum(n2); n1+=s2; n2+=s1; c++); print1(c,", "); ); }

Formula

n1(i) = n1(i-1) + digsum(n2(i-1)), n2(i) = n2(i-1) + digsum(n1(i-1))