A256577 Sum_{k>=0} (d_k)^(k+1)*10^k, where Sum_{k>=0} (d_k)*10^k is the decimal expansion of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 490

Offset: 0

Author

Michael De Vlieger, Apr 02 2015

Keywords

• base
• nonn
• easy

Comments

a(n) = n when 0 <= n < 20 or 10^i <= n < 10^i + 20 for some i>1.

a(n) = n if and only if every digit of n (in base 10), except possibly the ones digit, is 0 or 1. Otherwise, n < a(n). - Danny Rorabaugh, Apr 02 2015

Examples

			a(19) = 1^2 * 10^1 + 9^1 * 10^0 = 19.
a(20) = 2^2 * 10^1 + 0^1 * 10^0 = 40.
a(40) = 4^2 * 10^1 + 0^1 * 10^0 = 160.
a(199) = 1^3 * 10^2 + 9^2 * 10^1 + 9^1 * 10^0 = 100 + 810 + 9 = 919.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A066566 (first 39 terms identical).

Cf. A255073 (primes that remain prime, no carry).

Programs

Mathematica

Array[Total@ MapIndexed[#1^(#2)*10^(#2 - 1) & @@ {#1, First[#2]} &, Reverse@ IntegerDigits[#]] &, 71, 0] (* Michael De Vlieger, Nov 16 2022 *)

PARI

vector(80, n, d = digits(n); sum(k=1, #d, d[k]^(#d-k+1)*10^(#d-k))) \\ Michel Marcus, Apr 09 2015

Extensions

Name and comments corrected by Paul Tek, Apr 11 2015