%I A127485
%S A127485 1,2,13,22,23,98,253,343,573,638,702,1322,1862,2543,2638,2758,2792,2912,
%T A127485 3093,3158,3242,3578,3968,4382,5013,6503,7048,7877,8372,8912,9022,9207,
%U A127485 10298,10443,11538,12482,13077,13078,13868,14267,14268,14323,14783
%N A127485 Numbers n such that A127483(n) = A127483(n+1) - 1 = A127483(n+2) - 2.
%C A127485 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 k = {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. Triplets 
               in A127483(k) start with numbers k = a(n). Quadruplets in A127483(k) 
               start with k = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,
               54662,...} = A127486.
%t A127485 Select[Range[30000],PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&&PrimeQ[(#+2)^3+(#+3)^2]&]
%Y A127485 Cf. A100705, A100662, A127483, A127484, A127486.
%Y A127485 Sequence in context: A061871 A084651 A085509 this_sequence A061385 A156179 
               A090519
%Y A127485 Adjacent sequences: A127482 A127483 A127484 this_sequence A127486 A127487 
               A127488
%K A127485 nonn
%O A127485 1,2
%A A127485 Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 16 2007