A127485 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2.

1, 2, 13, 22, 23, 98, 253, 343, 573, 638, 702, 1322, 1862, 2543, 2638, 2758, 2792, 2912, 3093, 3158, 3242, 3578, 3968, 4382, 5013, 6503, 7048, 7877, 8372, 8912, 9022, 9207, 10298, 10443, 11538, 12482, 13077, 13078, 13868, 14267, 14268, 14323, 14783

Offset: 1

Author

Alexander Adamchuk, Jan 16 2007

Keywords

• nonn

Comments

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, triples 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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Magma

f:=func; [k:k in [1..15000]|f(k) and f(k+1) and f(k+2)]; // Marius A. Burtea, Jan 20 2020

Mathematica

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