A298168 The first of three consecutive triangular numbers the sum of which is equal to the sum of three consecutive primes.

1, 6, 28, 55, 66, 253, 351, 496, 595, 946, 2278, 2775, 3403, 3486, 4851, 6105, 7626, 9045, 11935, 14706, 23871, 33670, 39903, 41328, 43365, 46056, 46971, 50721, 53301, 60378, 64261, 87990, 91378, 92665, 114481, 124251, 126253, 126756, 134421, 141246, 144991

Offset: 1

Author

Colin Barker, Jan 14 2018

Keywords

• nonn

Examples

			31 is in the sequence because 6+10+15 (consecutive triangular numbers) = 31 = 7+11+13 (consecutive primes).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..300 from Colin Barker)

Crossrefs

Cf. A000040, A000217, A298169.

Programs

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 *)

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)