A115883 The n-th prime minus n gives a triangular number.

1, 2, 4, 5, 7, 13, 34, 37, 46, 62, 104, 111, 210, 259, 274, 296, 306, 439, 488, 502, 513, 751, 763, 817, 969, 998, 1132, 1231, 1405, 1586, 1849, 1982, 2107, 2488, 2578, 2695, 2732, 2752, 2989, 3008, 3079, 3322, 3958, 4201, 4628, 5035, 5594, 5722, 5929

Offset

1,2

Links

Harvey P. Dale and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 500 terms from Harvey P. Dale)

Example

prime(13)-13 = 41-13 = 28 = T(7).

Mathematica

Flatten[Position[Table[Prime[n]-n, {n, 6000}], _?(IntegerQ[(Sqrt[ 8#+1]- 1)/2]&)]] (* Harvey P. Dale, Oct 08 2012 *)
pntQ[{a_, b_}]:=OddQ[Sqrt[8(a-b)+1]]; Module[{nn=6000}, Select[Thread[ {Prime[ Range[nn]], Range[nn]}], pntQ]][[All, 2]] (* Harvey P. Dale, Dec 20 2019 *)

Prog

(PARI) isok(n) = ispolygonal(prime(n) - n, 3); \\ Michel Marcus, Jan 25 2014

Crossrefs

Cf. A064370, A115882, A115887.

Sequence in context: A115008 A275368 A332296 * A063508 A356849 A101724

Adjacent sequences: A115880 A115881 A115882 * A115884 A115885 A115886

Keyword

nonn

Author

Giovanni Resta, Feb 06 2006

Status

approved