A278935 Least number k = concat(x,y) such that k = n*x*y - x - y, -1 if such a number does not exist.

126, 84, 63, 3231, 42, 4154, 2143, 1143, 4105263158, 6440909347642, 21, 11, 2077, 1077, 18063, 1206, 16056, 105882353, 2052631579, 43304763, 3220454673821, 8044, 12042, 30411, 6039, 5037593985, 321603571507896, 5035, 14033492823, 3033, 17403126122889, 20713030303119

Offset

2,1

Comments

MSD of y can be 0.

a(n) = -1 if n is divisible by 40: see StackExchange link. - Robert Israel, Nov 14 2025

Links

Giovanni Resta, Table of n, a(n) for n = 2..100 (all terms <10^50)

R. Israel et al, Does 10^d + 1 have any divisors == -1 (mod 40), Mathematics StackExchange, Nov 2025.

Example

a(5) = 3231 = concat(3,231) and 5*3*231 - 3 - 231 = 3231;
a(18) = 16056 = concat(16,056) and 18*16*56 - 16 - 56 = 16056.

Maple

with(numtheory): P:=proc(q) local j, k, s, t, n, ok;
for j from 2 to q do ok:=1; for n from 1 to q do if ok=0 then break; else
for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k);
if j*s*t-s-t=n then print(n); ok:=0; break; fi; od; fi; od; od; end: P(10^6);

Crossrefs

Cf. A279058.

Sequence in context: A348898 A267403 A267342 * A267395 A176303 A157321

Adjacent sequences: A278932 A278933 A278934 * A278936 A278937 A278938

Keyword

nonn,base

Author

Paolo P. Lava, Dec 02 2016

Extensions

a(10), a(11), a(19)-a(22), a(27), a(28), a(30), a(32), a(33) by Giovanni Resta, Dec 05 2016

Status

approved