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Search: id:A127483
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| 1, 2, 3, 4, 8, 9, 13, 14, 15, 17, 22, 23, 24, 25, 30, 32, 34, 35, 38, 39, 42, 45, 50, 58, 60, 64, 65, 79, 83, 85, 88, 90, 92, 94, 98, 99, 100, 102, 113, 115, 122, 125, 127, 130, 133, 134, 137, 140, 144, 147, 148, 153, 154, 157, 164, 167, 170, 178, 179, 184, 190, 193
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 a(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 start with n = {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,...} = A127484, or numbers n such that a(n) = a(n+1) - 1. Triplets start with n = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485, or numbers n such that a(n) = a(n+1) - 1 = a(n+2) - 2. Quadruplets start with n = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,...} = A127486.
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MATHEMATICA
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Select[Range[1000], PrimeQ[ #^3+(#+1)^2]&]
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CROSSREFS
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Cf. A100705, A100662, A127484, A127485, A127486.
Sequence in context: A023786 A018231 A085256 this_sequence A130804 A022999 A057844
Adjacent sequences: A127480 A127481 A127482 this_sequence A127484 A127485 A127486
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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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