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

0,2

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

Links

Table of n, a(n) for n=0..4.

Formula

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

Example

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

Prog

(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, ", "); ); }

Crossrefs

Cf. A004207, A272235

Sequence in context: A121693 A190297 A072259 * A283164 A242983 A167533

Adjacent sequences: A272230 A272231 A272232 * A272234 A272235 A272236

Keyword

nonn,base,more

Author

Anthony Sand, Apr 23 2016

Status

approved