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A165966
Triangular numbers that are sums of twin prime pairs.
3
36, 120, 276, 300, 2556, 3240, 5460, 8256, 12720, 23436, 26796, 34980, 41616, 46056, 56616, 59340, 103740, 122760, 139656, 147696, 157080, 185136, 195000, 231540, 277140, 333336, 353220, 386760, 401856, 516636, 609960, 860016, 1001820
OFFSET
1,1
COMMENTS
All terms are multiples of 12.
LINKS
FORMULA
a(n) = A105174(n)*(A105174(n) + 1)/2.
EXAMPLE
36 = 8*9/2 is a term since it is triangular and the sum of the twin primes 17 and 19.
120 = 15*16/2 is a term since it is triangular and the sum of the twin primes 59 and 61.
MATHEMATICA
tri[n_] := n*(n+1)/2; Select[tri /@ Range[10^3], And @@ PrimeQ[#/2 + {-1, 1}] &] (* Amiram Eldar, Dec 27 2019 *)
PROG
(PARI) lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg, ", ")); ); } \\ Michel Marcus, Oct 16 2013
CROSSREFS
Subsequence of A111163 and of A054735.
Sequence in context: A350500 A287861 A242356 * A307939 A254146 A173420
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 01 2009
STATUS
approved