A319599 Numbers k such that k mod (2, 3, 4, ... , i+1) = (d_i, d_i-1, ..., d_1), where d_1, d_2, ..., d_i are the digits of k, with MSD(k) = d_1 and LSD(k) = d_i.

0, 1, 10, 20, 1101, 1121, 11311, 31101, 40210, 340210, 4620020, 5431101, 7211311, 12040210, 24120020, 151651121, 165631101, 1135531101, 8084220020, 9117311311, 894105331101, 15379177511311, 58086024120020

Offset

1,3

Comments

a(24) > 10^50, if it exists (cf. A284815). - Giovanni Resta, Oct 19 2025

Links

Table of n, a(n) for n=1..23.

Example

5431101 is a term because:
  5431101 mod 2 = 1, 5431101 mod 3 = 0, 5431101 mod 4 = 1,
  5431101 mod 5 = 1, 5431101 mod 6 = 3, 5431101 mod 7 = 4, 5431101 mod 8 = 5.

Maple

P:=proc(q) local a, i, j, n, ok; print(0); print(1); for n from 1 to q do
for i from 0 to 1 do a:=10*n+i; ok:=1; for j from 1 to ilog10(a)+1 do
if (a mod 10)<>((10*n+i) mod (j+1)) then ok:=0; break; else
a:=trunc(a/10); fi; od; if ok=1 then print(10*n+i); break; fi;
od; od; end: P(10^12);

Prog

(Julia)
function ok(n::Integer) return all(n%(i+1) == d for (i, d) in enumerate(digits(n))) end
println([n for n in 0:3*10^7 if ok(n)]) # Michael S. Branicky, Oct 17 2025
(Python)
def ok(n): return all(n%i == di for i, di in enumerate(map(int, str(n)[::-1]), 2))
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Oct 17 2025

Crossrefs

Cf. A266181, A284815.

Sequence in context: A018990 A280882 A335802 * A160479 A085222 A085221

Adjacent sequences: A319596 A319597 A319598 * A319600 A319601 A319602

Keyword

nonn,base,more

Author

Paolo P. Lava, Sep 24 2018

Extensions

Offset corrected, a(22)-a(23) added by Giovanni Resta, Oct 19 2025

Status

approved