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A298169
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The first of three consecutive primes the sum of which is equal to the sum of three consecutive triangular numbers.
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12
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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31 is in the sequence because 7+11+13 (consecutive primes) = 31 = 6+10+15 (consecutive triangular numbers).
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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