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A371029
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Numbers m such that if k = 27*m^3 + 3*m then k-1 and k+1 are primes.
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0
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1, 5, 6, 7, 13, 29, 39, 40, 45, 81, 120, 122, 127, 142, 143, 205, 214, 241, 293, 334, 341, 390, 391, 408, 486, 502, 506, 510, 577, 632, 640, 655, 669, 675, 686, 711, 720, 792, 793, 794, 802, 851, 859, 891, 901, 909, 972, 974, 992, 1000, 1041, 1078, 1082, 1096, 1099, 1111, 1206, 1258, 1280, 1423
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OFFSET
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1,2
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COMMENTS
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Conjecture: this sequence is infinite.
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LINKS
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EXAMPLE
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1 is this sequence because 27*1^3 + 3*1 = 30 has 2 prime neighbors 29 and 31.
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MATHEMATICA
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Select[Range[1500], And @@ PrimeQ[27*#^3 + 3*# + {-1, 1}] &] (* Amiram Eldar, Mar 26 2024 *)
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PROG
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(Magma) [m: m in [1..1500] | IsPrime(27*m^3+3*m-1) and IsPrime(27*m^3+3*m+1)];
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CROSSREFS
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Numbers m such that (n*m)^n + n*m has 2 prime neighbors: A040040 (n=1); no sequence (n=2) in OEIS; this sequence (n=3); no sequence (n=4) in OEIS.
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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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