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 A159047 Primes which are triangular numbers plus 3. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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: A034050 A107689 A154834 * A219971 A073337 A128067 Adjacent sequences:  A159044 A159045 A159046 * A159048 A159049 A159050 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Apr 03 2009 STATUS approved

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)