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URL: https://oeis.org/A298168

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A298168
The first of three consecutive triangular numbers the sum of which is equal to the sum of three consecutive primes.
12
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
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 14 2018
STATUS
approved