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A116936 Numbers n such that in the 3 X 3 square arrangement of the 9 primes prime(n),...,prime(n+8), the 3 row sums, 3 column sums and 2 diagonal sums are all prime. 1

%I #16 Jan 25 2018 02:55:00

%S 417979,5828779,6778746,9866895,20250501,20583048,20688247,26172783,

%T 35972619,60914800,67162336,78692065,78798340,101105398,104627288,

%U 126648015,131916133,138376385,170592575,172837628,180756151

%N Numbers n such that in the 3 X 3 square arrangement of the 9 primes prime(n),...,prime(n+8), the 3 row sums, 3 column sums and 2 diagonal sums are all prime.

%C n such that prime(n)+prime(n+1)+prime(n+2), prime(n+3)+prime(n+4)+prime(n+5), prime(n+6)+prime(n+7)+prime(n+8), prime(n)+prime(n+3)+prime(n+6), prime(n+1)+prime(n+4)+prime(n+7), prime(n+2)+prime(n+5)+prime(n+8), prime(n)+prime(n+4)+prime(n+8), prime(n+2)+prime(n+4)+prime(n+5) are all prime. - _Robert Israel_, Jan 24 2018

%e 417979 is in the sequence because prime(417979) = 6080051 and we have this 3 X 3 square with the desired property:

%e .

%e 6080051 6080059 6080069 => 18240179

%e .

%e 6080131 6080141 6080147 => 18240419

%e .

%e 6080149 6080153 6080161 => 18240463

%e // || || || \\

%e 18240359 VV VV VV 18240353

%e 18240331 18240353 18240377

%Y Cf. A097231.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 27 2006

%E Extended by _D. S. McNeil_, Dec 16 2010

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Last modified July 15 11:16 EDT 2024. Contains 374332 sequences. (Running on oeis4.)