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A216898 a(n) = smallest number k such that both k - n^2 and k + n^2 are primes. 2

%I

%S 2,4,7,14,21,28,43,52,67,86,111,150,149,180,201,232,267,312,329,366,

%T 411,446,487,532,587,654,705,742,787,852,911,972,1029,1118,1185,1242,

%U 1313,1372,1473,1528,1603,1692,1769,1852,1941,2032,2127,2212,2317,2412,2503

%N a(n) = smallest number k such that both k - n^2 and k + n^2 are primes.

%C Note that a(11) = 150 and a(12) = 149. Up to n = 10^6, this is the only case where a(n) > a(n+1). What about general case of a(n) < a(n+1)?

%C First differences are almost linear with n hence the only case with a(n) > a(n+1) is n = 11. - _Zak Seidov_, May 19 2014

%H Zak Seidov, <a href="/A216898/b216898.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A087711(n^2). - _T. D. Noe_, Sep 19 2012

%e a(11) = 150 because both 150 - 11^2 = 29 and 150 + 11^2 = 271 are primes.

%e a(12) = 149 because both 149 - 12^2 = 5 and 149 + 12^2 = 293 are primes.

%t Table[If[n < 1, 2, m = n^2 + 1; While[!PrimeQ[m - n^2] || !PrimeQ[m + n^2], m = m + 2]; m], {n, 0, 100}]

%Y Cf. A087711.

%K nonn

%O 0,1

%A _Zak Seidov_, Sep 19 2012

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)