|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|