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 k = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485. Quadruplets in A127483(k) start with numbers k = a(n).

For n>1 the final digit of all listed terms of a(n) is 2 or 7. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 16 2007

f[s_]:=s^3+(s+1)^2; Do[If[PrimeQ[f[n]]&&PrimeQ[f[n+1]]&&PrimeQ[f[n+2]]&&PrimeQ[f[n+3]], Print[n]], {n, 1, 100000}]

Cf. A100705, A100662, A127483, A127484, A127485.

Sequence in context: A110802 A013727 A028692 this_sequence A078398 A060619 A092212

Adjacent sequences: A127483 A127484 A127485 this_sequence A127487 A127488 A127489

hard,nonn

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

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