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Search: id:A127484
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| 1, 2, 3, 8, 13, 14, 22, 23, 24, 34, 38, 64, 98, 99, 133, 147, 153, 178, 232, 253, 254, 297, 328, 343, 344, 367, 407, 498, 573, 574, 582, 587, 624, 638, 639, 653, 668, 679, 702, 703, 759, 772, 793, 797, 849, 874, 944, 958, 1023, 1058, 1067, 1087, 1203, 1212, 1322
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OFFSET
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1,2
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COMMENT
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A127483(n) = {1,2,3,4,8,9,13,14,15,17,22,23,24,25,30,32,34,35,38,39,42,45,50,...} are the numbers n such that A100705(n) = n^3 + (n+1)^2 is prime. Corresponding primes of the form n^3 + (n+1)^2 are listed in A100662(n) = {5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, ...}. Note that there are many consecutive twins, triplets and quadruplets in A127483(n). For example: (1,2,3,4), {8,9}, {13,14,15}, {22,23,24,25}, {34,35}, {38,39}, {64,65}, {98,99,100}. Twins in A127483(k) start with numbers k = a(n). Triplets in A127483(k) start with k = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485, or numbers n such that a(k) = a(k+1) - 1 = a(k+2) - 2. Quadruplets in A127483(k) start with k = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,...} = A127486.
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MATHEMATICA
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Select[Range[3000], PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&]
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CROSSREFS
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Cf. A100705, A100662, A127483, A127485, A127486.
Sequence in context: A134683 A067853 A086590 this_sequence A080478 A002053 A102315
Adjacent sequences: A127481 A127482 A127483 this_sequence A127485 A127486 A127487
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 16 2007
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