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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A138873 A091307 A254879 * A317478 A353901 A081537
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 14 2018
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)