login
A298169
The first of three consecutive primes the sum of which is equal to the sum of three consecutive triangular numbers.
12
2, 7, 31, 61, 73, 271, 373, 521, 619, 983, 2341, 2843, 3469, 3559, 4943, 6211, 7741, 9173, 12073, 14869, 24083, 33923, 40177, 41611, 43651, 46349, 47269, 51031, 53623, 60719, 64613, 88397, 91801, 93089, 114941, 124739, 126751, 127249, 134923, 141769, 145517
OFFSET
1,1
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 7+11+13 (consecutive primes) = 31 = 6+10+15 (consecutive triangular numbers).
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, listput(L, p))); Vec(L)
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 14 2018
STATUS
approved