A370520 Triangular numbers (A000217) in A353729.

1, 3, 6, 55, 66, 666, 1128, 1326, 2346, 31626, 133386, 193131, 212226, 236328, 283128, 416328, 881128, 1211346, 1222266, 1466328, 1777555, 2263128, 11293128, 14191128, 16111326, 16316328, 22121226, 22261128, 26263128, 31621128, 32292666, 33321366, 33533955, 39139128

Offset

1,2

Comments

Intersection of A000217 and A353729.

The sequence is infinite because the numbers T(1327) = 881128, T(13327) = 88811128, T(133327) = 8888111128, ..... are terms.

Also, the numbers T(651) = 212226, T(6651) = 22121226, T(66651) = 2221211226, T(666651) = 222212111226.... or T(672) = 226128, T(6672) = 22261128, T(66672) = 2222611128, ... are terms.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

2346 = A000217(68) and 346 = 2*173, 246 = 3*82, 234 = 6*39, so 2346 is a term.

Maple

filter:= proc(n) local L, d, i, j;
  L:= convert(n, base, 10); d:= nops(L);
  for i from 1 to d do
    if L[i] = 0 or add(L[j]*10^(j-1), j=1..i-1)+add(L[j]*10^(j-2), j=i+1..d) mod L[i] <> 0
       then return false
  fi od:
  true
end proc:
select(filter, [seq(i*(i+1)/2, i=1..10000)]); # Robert Israel, Feb 27 2025

Prog

(Magma) ints:=func<n| n eq 0 select[0] else Intseq(n)>; f:=func<n, i|Seqint([ints(n)[j]:j in [1..#ints(n)]|j ne (#ints(n)-i+1)])>; [p:p in [s*(s+1) div 2:s in [1..10000]]|not 0 in ints(p) and forall{i:i in [1..#ints(p)]|IsIntegral( f(p, i)/ ints(p)[(#Intseq(p)-i+1)] )}];

Crossrefs

Cf. A000217, A353729, A367451.

Sequence in context: A051641 A003098 A045914 * A303351 A067610 A067609

Adjacent sequences: A370517 A370518 A370519 * A370521 A370522 A370523

Keyword

nonn,base,changed

Author

Marius A. Burtea, Feb 27 2024

Status

approved