A110891 Numbers of the form prime(n) + prime(n+1) - 2 that are also triangular numbers, T(k) = k(k+1)/2.

3, 6, 10, 28, 66, 136, 666, 1540, 2278, 3160, 3486, 4186, 5050, 6328, 8128, 9730, 11476, 13366, 15400, 16110, 24090, 24976, 27730, 29646, 32896, 37950, 39340, 46360, 69378, 76636, 81406, 84666, 95266, 98346, 100576, 111628, 123256, 128778

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

a(1) = 3 because prime(1) + prime(2) - 2 = 2 + 3 - 2 = 3 = T(2);
a(2) = 6 because prime(2) + prime(3) - 2 = 3 + 5 - 2 = 6 = T(3);
a(5) = 66 because prime(11) + prime(12) - 2 = 31 + 37 - 2 = 66 = T(11);
a(6) = 136 because prime(19) + prime(20) - 2 = 67 + 71 - 2 = 136 = T(16).

Mathematica

Select[Table[Prime[n] + Prime[n + 1] - 2, {n, 7000}], IntegerQ[Sqrt[1 + 8# ]] &] (* Ray Chandler, Oct 07 2005 *)
Select[Total[#]-2&/@Partition[Prime[Range[10000]], 2, 1], OddQ[ Sqrt[ 8#+1]]&] (* Harvey P. Dale, Sep 03 2016 *)

Crossrefs

Cf. A000217 (triangular numbers), A001043 (sum of successive primes).

Sequence in context: A068866 A137173 A116544 * A197435 A240514 A115887

Adjacent sequences: A110888 A110889 A110890 * A110892 A110893 A110894

Keyword

easy,nonn

Author

Giovanni Teofilatto, Sep 20 2005

Extensions

Edited and extended by Ray Chandler, Oct 07 2005

Status

approved