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

1,2

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

Cf. A000040, A000217, A298169.

Sequence in context: A377095 A091307 A254879 * A317478 A353901 A081537

Adjacent sequences: A298165 A298166 A298167 * A298169 A298170 A298171

Keyword

nonn

Author

Colin Barker, Jan 14 2018

Status

approved