A159047 Primes which are triangular numbers plus 3.

3, 13, 31, 139, 193, 409, 499, 823, 1381, 1543, 2083, 2281, 3163, 3919, 6673, 7753, 9319, 9733, 17581, 19309, 21739, 22369, 24979, 27031, 27733, 30631, 39343, 40189, 51043, 53959, 54949, 57973, 62131, 67531, 70879, 81409, 85081, 86323, 91381

Offset

1,1

Comments

For n>1, a(n)== 1 (mod 6). [Proof: the triangular numbers are {0,1,3,4} (mod 6), see A104686. 3 plus triangular numbers in the same set, and only those == 1 (mod 6) can be primes.] - Zak Seidov, Oct 16 2015

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

13=10+3, 31=28+3, 139=136+3, 193=190+3, 409=406+3, ...

Mathematica

s=0; lst={}; Do[s+=n; p=s+3; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 7!}]; lst
Select[Table[n*(n + 1)/2 + 3, {n, 0, 250}], PrimeQ] (* G. C. Greubel, Jul 13 2017 *)
Select[Accumulate[Range[0, 500]]+3, PrimeQ] (* Harvey P. Dale, Jul 30 2018 *)

Prog

(PARI) for(n=0, 1e3, if(isprime(k=3+n*(n+1)/2), print1(k", "))) \\ Altug Alkan, Oct 16 2015

Crossrefs

Cf. A000217, A055469, A055472.

Sequence in context: A107689 A339945 A154834 * A219971 A073337 A128067

Adjacent sequences: A159044 A159045 A159046 * A159048 A159049 A159050

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 03 2009

Status

approved