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%I #9 Jan 20 2020 13:01:41
%S 1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,144487,
%T 181777,205897,210022,213982,250517,263717,344092,409697,454607,
%U 568777,643677,665917,702947,749967,824167,858187,887677,888427,997787,1075537
%N Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2 = A127483(k+3) - 3.
%C 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).
%C For n>1 the final digit of all listed terms of a(n) is 2 or 7. - _Alexander Adamchuk_, Jan 16 2007
%H Amiram Eldar, <a href="/A127486/b127486.txt">Table of n, a(n) for n = 1..3000</a>
%t 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}]
%Y Cf. A100705, A100662, A127483, A127484, A127485.
%K hard,nonn
%O 1,2
%A _Alexander Adamchuk_, Jan 16 2007
%E More terms from _Alexander Adamchuk_, Jan 16 2007
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