A378513 a(1) = 1, a(n) = a(n-1) + n if all the digits of a(n-1) do not share a divisor greater than 1. Otherwise, a(n) = a(n-1) divided by the gcd of all its individual digits.

1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 22, 11, 24, 12, 27, 43, 60, 10, 29, 49, 70, 10, 33, 11, 36, 12, 39, 13, 42, 21, 52, 84, 21, 55, 11, 47, 84, 21, 60, 10, 51, 93, 31, 75, 120, 166, 213, 261, 310, 360, 120, 172, 225, 279, 334, 390, 130, 188, 247, 307, 368, 430

Offset: 1

Author

Stuart Coe, Nov 29 2024

Keywords

• nonn
• base
• look

Comments

It can be shown that this sequence will grow indefinitely: Once it has reached a given number of digits in length, it cannot drop below that number of digits. Regardless of the number of times the number is reduced by dividing by GCDs, n will inevitably be great enough to increase a(n) to a larger and larger number of digits in length.

Examples

			a(37) = 47 + 37, because the digits of 47 do not share a factor greater than 1.
a(38) = 84 / 4 = 21, because the gcd of 8 and 4 is 4.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052423 (gcd of digits).

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 1, (t-> (g->
      `if`(g=1, t+n, t/g))(igcd(convert(t, base, 10)[])))(a(n-1)))
    end:
seq(a(n), n=1..62);  # Alois P. Heinz, Nov 29 2024

Mathematica

Module[{n = 1, g}, NestList[If[n++; (g = GCD @@ IntegerDigits[#]) == 1, # + n, #/g] &, 1, 100]] (* Paolo Xausa, Dec 16 2024 *)

PARI

lista(nn) = my(v=vector(nn)); v[1] = 1; for (n=2, nn, my(g=gcd(digits(v[n-1]))); if (g == 1, v[n] = v[n-1]+n, v[n] = v[n-1]/g);); v; \\ Michel Marcus, Dec 09 2024