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 A242137 Numbers n such that there are no triangular numbers strictly between n^2 and n^2 + n. 1
 0, 1, 2, 4, 6, 9, 11, 14, 16, 21, 23, 26, 28, 33, 35, 38, 40, 45, 50, 52, 55, 57, 62, 64, 67, 69, 74, 79, 81, 84, 86, 91, 93, 96, 98, 103, 108, 110, 115, 120, 122, 125, 127, 132, 134, 137, 139, 144, 149, 151, 154, 156, 161, 163, 166, 168, 173, 178, 180, 185, 190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n>2, a(n+1) - a(n) = either 2 or 3 or 5 (conjecture; checked up to a(n) = 2^32). LINKS Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 MATHEMATICA triQ[n_] := IntegerQ@ Sqrt[8n + 1]; fQ[n_] := Union[ triQ@# & /@ Range[n^2 + 1, n^2 + n - 1]] == {False}; Join[{0, 1}, Select[ Range@ 200, fQ]] (* Robert G. Wilson v, Jan 22 2016 *) PROG (Python) t = prev = 0 for n in range(1000000):   sq = n*n   ob = sq + n   s = 0   while 1:     tn = t*(t+1)/2     if tn > sq:         if tn < ob:             s = 1         break     t+=1   t-=1   if s==0:     print str(n)+', ',     #d = n-prev     #if d!=2 and d!=3 and d!=5: print n, d     #prev = n (PARI) isokt(n) = for (k=n^2+1, n^2+n-1, if (ispolygonal(k, 3), return (0))); return(1); \\ Michel Marcus, Aug 16 2014 CROSSREFS Cf. A000217, A000290, A002378. Sequence in context: A091626 A085223 A163057 * A138326 A274214 A276223 Adjacent sequences:  A242134 A242135 A242136 * A242138 A242139 A242140 KEYWORD nonn AUTHOR Alex Ratushnyak, Aug 16 2014 STATUS approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)