OFFSET
1,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..300 from Colin Barker)
EXAMPLE
31 is in the sequence because 6+10+15 (consecutive triangular numbers) = 31 = 7+11+13 (consecutive primes).
MATHEMATICA
(#(#+1))/2&/@(Select[(Sqrt[3] Sqrt[8#-5]-9)/6&/@(Total/@Partition[Prime[ Range[ 20000]], 3, 1]), IntegerQ]) (* Harvey P. Dale, Jun 22 2019 *)
PROG
(PARI) L=List(); forprime(p=2, 400000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(24*t-15, &sq) && (sq-9)%6==0, u=(sq-9)\6; listput(L, u*(u+1)/2))); Vec(L)
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 14 2018
STATUS
approved