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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.
2
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.
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 03 2003
EXTENSIONS
More terms from David Wasserman, Jul 26 2004
STATUS
approved