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A088498 Numbers k such that k^2 + k - 1 and k^2 + k + 1 are twin primes and (k + 1)*(k + 1) + k + 1 - 1 and (k + 1)*(k + 1) + k + 1 + 1 are also twin primes.

%I A088498 #16 Feb 12 2022 16:10:41
%S A088498 2,5,20,455,1364,2204,2450,2729,8540,18485,32198,32318,32780,45863,
%T A088498 61214,72554,72560,82145,83258,86603,91370,95198,125333,149330,176888,
%U A088498 182909,185534,210845,225665,226253,288419,343160,350090,403940,411500
%N A088498 Numbers k such that k^2 + k - 1 and k^2 + k + 1 are twin primes and (k + 1)*(k + 1) + k + 1 - 1 and (k + 1)*(k + 1) + k + 1 + 1 are also twin primes.
%H A088498 Amiram Eldar, <a href="/A088498/b088498.txt">Table of n, a(n) for n = 1..10000</a>
%e A088498 20 is a term since 20^2 + 20 - 1 = 419, 419 and 421 are twin primes, 21^2 + 21 - 1 = 461, and 461 and 463 are also twin primes.
%t A088498 Select[ Range[510397], PrimeQ[ #^2 + # - 1] && PrimeQ[ #^2 + # + 1] && PrimeQ[ #^2 + 3# + 1] && PrimeQ[ #^2 + 3# + 3] & ]
%t A088498  Select[Range[412000],AllTrue[Flatten[{#^2+#+{1,-1},(#+1)(#+1)+#+{0,2}}], PrimeQ]&] (* _Harvey P. Dale_, Feb 12 2022 *)
%Y A088498 Cf. A088485.
%K A088498 base,nonn
%O A088498 1,1
%A A088498 _Pierre CAMI_, Nov 11 2003
%E A088498 Corrected and extended by _Ray Chandler_ and _Robert G. Wilson v_, Nov 12 2003