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%I #8 Jan 19 2019 04:14:58
%S 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,
%T 64,65,79,83,85,88,90,92,94,98,99,100,102,113,115,122,125,127,130,133,
%U 134,137,140,144,147,148,153,154,157,164,167,170,178,179,184,190,193
%N Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.
%C 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 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}.
%C 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.
%C 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.
%C Quadruplets start with n = {1,22,13077,14267,16092,16267,162,...} = A127486.
%H Ivan Neretin, <a href="/A127483/b127483.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[1000],PrimeQ[ #^3+(#+1)^2]&]
%Y Cf. A100705, A100662, A127484, A127485, A127486.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Jan 16 2007