A298487 a(n) is the least number with persistence n as defined using A114570.

1, 10, 19, 43, 67, 83, 92, 293, 691, 958, 7849, 49670, 94976, 880096, 7090761, 80890670, 798992994, 9999069559, 808009099075, 8979948969844, 898989690790838

Offset

0,2

Comments

Repeat A114570 until one digit remains.

a(n) is the first number with persistence n in base 10.

a(n+1) <= Sum_{i=0..a(n)-1} 10^i showing the sequence is infinite.

a(n) does not necessarily pass through a(n-1) on the first step.

Links

Table of n, a(n) for n=0..20.

Example

a(5) = 83 because:
83 -> 8^2 + 3^1 = 67;
67 -> 6^2 + 7^1 = 43;
43 -> 4^2 + 3^1 = 19;
17 -> 1^2 + 9^1 = 10;
10 -> 1^2 + 0^1 =  1;
83 is the least integer to take 5 steps to get to 1 digit.

Prog

(PARI) a114570(n) = my(d=digits(n), k=#d); sum(i=1, k, d[i]^(k+1-i));
p(n) =  my(ip=0); while(n >= 10, n = a114570(n); ip++); ip;
a(n) = {my(k=1); while (p(k) != n, k++); k; } \\ Michel Marcus, Jan 25 2018

Crossrefs

Cf. A114570.

Sequence in context: A083705 A245003 A372096 * A359315 A082659 A088409

Adjacent sequences: A298484 A298485 A298486 * A298488 A298489 A298490

Keyword

nonn,base,more

Author

John Harmon, Jan 20 2018

Extensions

a(19) from Giovanni Resta, Jan 22 2018

a(20) from Giovanni Resta, Feb 01 2018

Status

approved