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

1,2

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.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A052423 (gcd of digits).

Sequence in context: A093178 A340086 A307153 * A339421 A336898 A300330

Adjacent sequences: A378510 A378511 A378512 * A378514 A378515 A378516

Keyword

nonn,base,look

Author

Stuart Coe, Nov 29 2024

Status

approved