1,2

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.

Select[Range[30000], PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&&PrimeQ[(#+2)^3+(#+3)^2]&]

Cf. A100705, A100662, A127483, A127484, A127486.

Sequence in context: A061871 A084651 A085509 this_sequence A061385 A156179 A090519

Adjacent sequences: A127482 A127483 A127484 this_sequence A127486 A127487 A127488

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 16 2007