A079838 a(1)=1 and for n>1, a(n) is the smallest multiple of a(n-1) which has no nonzero digit in common with a(n-1).

1, 2, 4, 8, 16, 32, 64, 128, 640, 1280, 6400, 12800, 64000, 128000, 640000, 1280000, 6400000, 12800000, 64000000, 128000000, 640000000, 1280000000, 6400000000, 12800000000, 64000000000, 128000000000, 640000000000, 1280000000000, 6400000000000, 12800000000000

Offset

1,2

Comments

The sequence is infinite and the pattern is visible after a(7): a(2n) = 2*a(2n-1) and a(2n+1) = 5*a(2n), n > 3.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,10).

Formula

G.f.: x*(2*x + 1)*(96*x^6 + 24*x^4 + 6*x^2 - 1)/(10*x^2 - 1). - Paolo Xausa, Aug 29 2025

Mathematica

LinearRecurrence[{0, 10}, 2^Range[0, 7], 30] (* Paolo Xausa, Aug 29 2025 *)

Prog

(PARI) nzd(k) = Set(select(x->(x != 0), digits(k)));
lista(nn) = my(va=vector(nn)); va[1]=1; for (n=2, nn, my(newa = va[n-1], k=1, sd = nzd(newa)); while (#setintersect(nzd(newa), sd), k++; newa=k*va[n-1]); va[n] = newa; ); va; \\ Michel Marcus, Aug 28 2025

Crossrefs

Sequence in context: A264791 A290851 A290670 * A109912 A079845 A278995

Adjacent sequences: A079835 A079836 A079837 * A079839 A079840 A079841

Keyword

base,nonn,easy

Author

Amarnath Murthy, Feb 15 2003

Extensions

Offset changed and more terms from Sean A. Irvine, Aug 27 2025

Status

approved