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 A244254 Positive integers n such that all the gaps prime(n+i+1) - prime(n+i) (i = 0..5) are triangular numbers. 6
 73262, 284773, 384110, 654181, 661578, 774253, 1224508, 1318737, 1468078, 1618409, 1645451, 1768023, 1870004, 1987951, 2166522, 2201378, 2319324, 2379233, 2478328, 2498215, 2832557, 3548643, 3606640, 3671993, 3692292 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: For any integer m > 0, there are infinitely many positive integers n such that all the gaps prime(n+i+1) - prime(n+i) (i = 0, ..., m-1) are triangular numbers. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..2600 EXAMPLE a(1) = 73262 with prime(73263) - prime(73262) = 927007 - 927001 = 3*4/2, prime(73264) - prime(73263) = 927013 - 927007 = 3*4/2, prime(73265) - prime(73264) = 927049 - 927013 = 8*9/2, prime(73266) - prime(73265) = 927077 - 927049 = 7*8/2 and prime(73267) - prime(73266) = 927083 - 927077 = 3*4/2. MATHEMATICA TQ[n_]:=IntegerQ[Sqrt[8n+1]] m=0; Do[Do[If[TQ[Prime[n+i+1]-Prime[n+i]]==False, Goto[aa]], {i, 0, 5}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 3692292}] CROSSREFS Cf. A000040, A000217. Sequence in context: A210009 A237701 A023185 * A184769 A242805 A250838 Adjacent sequences:  A244251 A244252 A244253 * A244255 A244256 A244257 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jun 24 2014 STATUS approved

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Last modified May 22 02:18 EDT 2022. Contains 353933 sequences. (Running on oeis4.)