A337016 a(0) = 0. Successive terms are double the previous, then with their digits incremented by 1.

0, 1, 3, 7, 25, 61, 233, 577, 2265, 5641, 22393, 55897, 2228105, 5567321, 22245753, 555102617, 2221316345, 55537437101, 222185985313, 5554821081737, 222110753274585, 5553326176510281, 22217763464131673, 555466371039374457, 222110438531898591025

Offset: 0

Author

Jamie Robert Creasey, Nov 21 2020

Keywords

• base
• nonn

Comments

If 9 appears anywhere in the decimal expansion of 2*a(n-1), we replace that digit with 10 upon incrementing by 1. See a(12) of the Examples section and A216556 for more information.

Examples

			To calculate a(12), double 55897 to get 111794, then increment the digits by 1 to get 2228105.
To calculate a(13), double 2228105 to get 4456210, then increment the digits by 1 to get 5567321.
		

Crossrefs

Cf. A000079, A061511, A089718.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(seq(
      l[-i]+1, i=1..nops(l)))))(convert(2*a(n-1), base, 10)))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 12 2020

Mathematica

NestList[FromDigits[Flatten@ Map[IntegerDigits, IntegerDigits[2 #] + 1]] &, 0, 24] (* Michael De Vlieger, Dec 11 2020 *)

PARI

digs(n) = if (n==0, [0], digits(n));
lista(nn) = {a = 0; print1(a, ", "); for (n=1, nn, a = eval(concat(apply(t->Str(t+1), digs(2*a)))); print1(a, ", "););} \\ Michel Marcus, Nov 28 2020

Formula

a(n) = A216556(2*a(n-1)), a(0) = 0.