A081974 a(1) = 1 and smallest number not occurring earlier such that the product of two neighboring terms is a distinct triangular number, where "distinct" means that a(n)*a(n+1) may not equal the product of any two previous consecutive terms.

1, 3, 2, 5, 9, 4, 7, 13, 6, 11, 21, 10, 12, 23, 45, 14, 27, 53, 26, 30, 33, 16, 31, 15, 20, 41, 81, 40, 52, 103, 51, 25, 49, 24, 47, 93, 46, 91, 60, 76, 151, 75, 37, 18, 112, 115, 57, 28, 55, 39, 19, 87, 43, 22, 133, 66, 58, 117, 35, 17, 8, 395, 126, 141, 70, 102, 90, 116, 231

Offset

1,2

Comments

Perhaps another re-arrangement of natural numbers.

Links

Table of n, a(n) for n=1..69.

Example

5 and 4 are the neighbors of 9 giving the triangular numbers 45 and 36 respectively.

Mathematica

istriang[n_] := With[{x = Floor[Sqrt[2*n]]}, n == x*(x + 1)/2];
nmax = 75;
Clear[a, used, tris];
a[_] = 0; used[_] = 0; tris[_] = 0; a[1] = 1; used[1] = 1;
For[i = 2, i <= nmax, i++, f = a[i-1]; j = 2; While[used[j] == 1 || !istriang[f*j] || tris[f*j] == 1, j++]; a[i] = j; used[j] = 1; tris[f*j] = 1];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, May 23 2024, after PARI code *)

Prog

(PARI) istriang(n) = local(x); x = floor(sqrt(2*n)); n == x*(x + 1)/2;
A = vector(75); used = vector(1000); tris = vector(50000); A[1] = 1; used[1] = 1; for (i = 2, 75, f = A[i - 1]; j = 2; while (used[j] || !istriang(f*j) || tris[f*j], j = j + 1); A[i] = j; used[j] = 1; tris[f*j] = 1); print(A)

Crossrefs

Cf. A081975, A081976, A081977.

Sequence in context: A160106 A243786 A278743 * A257883 A169755 A169748

Adjacent sequences: A081971 A081972 A081973 * A081975 A081976 A081977

Keyword

nonn

Author

Amarnath Murthy, Apr 03 2003

Extensions

More terms from David Wasserman, Jul 26 2004

Status

approved