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

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A064370, A115882, A115887.

Programs

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 *)

PARI

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