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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
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
Sequence in context: A107689 A339945 A154834 * A219971 A073337 A128067
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 26 03:59 EDT 2024. Contains 372807 sequences. (Running on oeis4.)