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A127484 Numbers k such that A127483(k) = A127483(k+1) - 1.

%I A127484 #12 Sep 08 2022 08:45:29
%S A127484 1,2,3,8,13,14,22,23,24,34,38,64,98,99,133,147,153,178,232,253,254,
%T A127484 297,328,343,344,367,407,498,573,574,582,587,624,638,639,653,668,679,
%U A127484 702,703,759,772,793,797,849,874,944,958,1023,1058,1067,1087,1203,1212,1322
%N A127484 Numbers k such that A127483(k) = A127483(k+1) - 1.
%C A127484 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.
%C A127484 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, ...}.
%C A127484 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 numbers k = a(n). Triplets in A127483(k) start with k = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485, or numbers n such that a(k) = a(k+1) - 1 = a(k+2) - 2. Quadruplets in A127483(k) start with k = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,...} = A127486.
%H A127484 Amiram Eldar, <a href="/A127484/b127484.txt">Table of n, a(n) for n = 1..10000</a>
%t A127484 Select[Range[3000],PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&]
%o A127484 (Magma) [k:k in [1..1350]|IsPrime(k^3+(k+1)^2) and IsPrime((k+1)^3+(k+2)^2)]; // _Marius A. Burtea_, Jan 20 2020
%Y A127484 Cf. A100705, A100662, A127483, A127485, A127486.
%K A127484 nonn
%O A127484 1,2
%A A127484 _Alexander Adamchuk_, Jan 16 2007