%I A127483
%S A127483 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,
%T A127483 64,65,79,83,85,88,90,92,94,98,99,100,102,113,115,122,125,127,130,133,
%U A127483 134,137,140,144,147,148,153,154,157,164,167,170,178,179,184,190,193
%N A127483 Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.
%C A127483 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.
%t A127483 Select[Range[1000],PrimeQ[ #^3+(#+1)^2]&]
%Y A127483 Cf. A100705, A100662, A127484, A127485, A127486.
%Y A127483 Sequence in context: A023786 A018231 A085256 this_sequence A130804 A022999 
               A057844
%Y A127483 Adjacent sequences: A127480 A127481 A127482 this_sequence A127484 A127485 
               A127486
%K A127483 nonn
%O A127483 1,2
%A A127483 Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 16 2007