A298487 - OEIS

%I #23 Feb 01 2018 04:21:23

%S 1,10,19,43,67,83,92,293,691,958,7849,49670,94976,880096,7090761,

%T 80890670,798992994,9999069559,808009099075,8979948969844,

%U 898989690790838

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

%C Repeat A114570 until one digit remains.

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

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

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

%e a(5) = 83 because:

%e 83 -> 8^2 + 3^1 = 67;

%e 67 -> 6^2 + 7^1 = 43;

%e 43 -> 4^2 + 3^1 = 19;

%e 17 -> 1^2 + 9^1 = 10;

%e 10 -> 1^2 + 0^1 =  1;

%e 83 is the least integer to take 5 steps to get to 1 digit.

%o (PARI) a114570(n) = my(d=digits(n), k=#d); sum(i=1, k, d[i]^(k+1-i));

%o p(n) =  my(ip=0); while(n >= 10, n = a114570(n); ip++); ip;

%o a(n) = {my(k=1); while (p(k) != n, k++); k;} \\ _Michel Marcus_, Jan 25 2018

%Y Cf. A114570.

%K nonn,base,more

%O 0,2

%A _John Harmon_, Jan 20 2018

%E a(19) from _Giovanni Resta_, Jan 22 2018

%E a(20) from _Giovanni Resta_, Feb 01 2018