A093799 a(1) = 1; a(n+1) is the smallest triangular number such that the greatest common divisor gcd(a(n+1), a(n)) is a triangular number itself.

1, 3, 6, 15, 21, 36, 55, 78, 105, 120, 153, 190, 210, 231, 276, 325, 378, 435, 465, 528, 595, 666, 741, 820, 903, 990, 1035, 1128, 1225, 1326, 1431, 1540, 1596, 1711, 1830, 1953, 2080, 2211, 2346, 2485, 2628, 2775, 2926, 3081, 3240, 3403, 3570, 3741, 3916

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

tri[n_] := n (n + 1)/2; triRoot[n_] := (-1 + Sqrt[8 n + 1])/2; triQ[n_] := IntegerQ @ Sqrt[8 n + 1]; f[n_] := Module[{k = triRoot[n] + 1}, While[!triQ[ GCD[n, (t = tri[k])]], k++]; t]; s = {1}; Nest[AppendTo[s, f[s[[-1]]]] &, s, 48] (* Amiram Eldar, Dec 23 2019 *)

Crossrefs

Cf. A000217.

Sequence in context: A069559 A117748 A061066 * A087359 A253651 A180322

Adjacent sequences: A093796 A093797 A093798 * A093800 A093801 A093802

Keyword

easy,nonn

Author

Jason Earls, May 18 2004

Extensions

Better description from Stefan Steinerberger, Feb 07 2006

Status

approved