A127486 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2 = A127483(k+3) - 3.

1, 22, 13077, 14267, 16092, 16267, 16282, 36387, 47012, 51912, 54662, 144487, 181777, 205897, 210022, 213982, 250517, 263717, 344092, 409697, 454607, 568777, 643677, 665917, 702947, 749967, 824167, 858187, 887677, 888427, 997787, 1075537

Offset: 1

Author

Alexander Adamchuk, Jan 16 2007

Keywords

• hard
• 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 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, Jan 16 2007

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000

Crossrefs

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

Programs

Mathematica

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}]

Extensions

More terms from Alexander Adamchuk, Jan 16 2007