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A344868
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Primes p that are equal to (prime(k)+2*prime(k+1)+3*prime(k+2))/2 for some k.
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1
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17, 101, 191, 227, 293, 431, 461, 557, 571, 757, 821, 863, 1039, 1193, 1213, 1277, 1291, 1307, 1373, 1483, 1499, 1721, 1811, 2239, 2293, 2309, 2447, 2689, 3167, 3181, 3547, 3617, 3701, 3881, 4243, 4441, 4703, 4723, 4871, 5651, 6079, 6101, 6133, 6829, 6907, 6997, 7523, 7853, 7879, 7949
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OFFSET
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1,1
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COMMENTS
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Corresponding values of k: 2, 10, 17, 20, 24, 33, 35, 41, 42, 53, 57, 60, 68, 77, 78, 81, 82, 83, 87, 93, 94, 104, 109, 131, 134, 135, 140, 153, 176, 177, 193, 196, 201, 209, 222, 233, 246, 247, 256, 288, 306, 307, 308, 337, 341, 344, 367, 379, 380, 382, 393, 395.
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LINKS
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EXAMPLE
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17 = (3 + 2*5 + 3*7)/2, 101 = (29 + 2*31 + 3*37)/2.
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MATHEMATICA
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s = {}; Do[If[PrimeQ[p = (Prime[k] + 2*Prime[k + 1] + 3*Prime[k + 2])/2], AppendTo[s, p]], {k, 400}]; s
Select[(#[[1]]+2#[[2]]+3#[[3]])/2&/@Partition[Prime[ Range[ 500]], 3, 1], PrimeQ] (* Harvey P. Dale, Jan 28 2022 *)
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PROG
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(PARI) {p = 3; q = 5; r = 7; for (k = 1, 400, if (isprime (P = (p + 2*q + 3*r)/2), print1 (P ", ")); p = q; q = r; r = nextprime (r + 2))}
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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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