A127483 Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.

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

Offset

1,2

Comments

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, triples 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,,...} = 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 = {1,22,13077,14267,16092,16267,162,...} = A127486.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[1000], PrimeQ[ #^3+(#+1)^2]&]

Crossrefs

Cf. A100705, A100662, A127484, A127485, A127486.

Sequence in context: A085256 A364810 A335761 * A130804 A022999 A244151

Adjacent sequences: A127480 A127481 A127482 * A127484 A127485 A127486

Keyword

nonn

Author

Alexander Adamchuk, Jan 16 2007

Status

approved