A392618 Greatest number m < A392568(n) such that A392568(n)*m equals the concatenation of the digit-wise multiplication, where the digits of the larger number are kept when m has no corresponding digit.

2, 3, 4, 5, 6, 7, 8, 92, 94, 89, 88, 88, 88, 88, 97, 98, 96, 97, 98, 98, 99, 99, 99, 99, 99, 99, 99, 924, 897, 924, 888, 964, 958, 984, 989, 986, 988, 989, 994, 9445, 8984, 997, 9666, 998, 998, 997, 998, 999, 999, 9854, 999

Offset

1,1

Comments

A392568 is the main entry for this problem.

Links

Max Alekseyev, Table of n, a(n) for n = 1..123

Index entries for sequences related to carryless arithmetic.

Prog

(PARI) /* Inefficient brute force, just for illustration. Returns the largest possible m < N if N is a term, or zero if not. [NB: The argument of the function isn't the index n of the terms here, but the corresponding larger number N = A392568(n).]*/
find_m(N)={ my(dn=digits(N), L=#dn, o, dwp); forstep(m=N-1, 2, -1, my(dp=digits(m*N));
  if (o = L - #dm=digits(m), dp[1..o] == dn[1..o] || next);
  #[0 | t <- dwp = [dm[i]*dn[i+o] | i<-[1..#dm]], t>9] == #dp - #dn || next;
  concat([if (t>9, digits(t), [t]) | t <- dwp]) == dp[o+1..-1] && return(m))}
A392618_upto(N) = [m | n <- [2..N], m = find_m(n)] \\ M. F. Hasler, Jan 25 2026

Crossrefs

Cf. A392568, A392040 (list of m*k).

Sequence in context: A098755 A028430 A290148 * A171717 A303369 A154701

Adjacent sequences: A392615 A392616 A392617 * A392619 A392620 A392621

Keyword

nonn,base

Author

Thomas Scheuerle, Jan 17 2026

Status

approved