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A272878
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a(0) = a(1) = 1, smallest a(n+1) > a(n-1) such that a(n)^2 + a(n+1)^2 is prime.
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1
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1, 1, 2, 3, 8, 5, 16, 9, 26, 11, 30, 13, 32, 15, 34, 21, 44, 29, 46, 39, 50, 43, 60, 61, 64, 71, 66, 79, 74, 81, 100, 83, 102, 95, 104, 101, 114, 109, 134, 115, 136, 135, 146, 139, 154, 141, 160, 143, 168, 155, 172, 165, 178, 173, 190, 177, 200, 189, 206, 199
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OFFSET
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0,3
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COMMENTS
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The associated primes 2, 5, 13, 73, 89, 281, 337, 757, 797, ... create a strictly increasing sequence. What is the rate of its growth?
Positive integers that are not in this sequence are 4, 6, 7, 10, 12, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, ... - Altug Alkan, May 14 2016
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LINKS
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MATHEMATICA
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a[0]=1; a[1]=1; a[n_]:=a[n]= Block[{t = a[n-2] + 1}, While[! PrimeQ[t^2 + a[n-1]^2], t++]; t]; Array[a, 80, 0] (* Giovanni Resta, May 08 2016 *)
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PROG
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(PARI) lista(nn) = {print1(x = 1, ", "); print1(y = 1, ", "); for (n=2, nn, z = x+1; while (! isprime(y^2+z^2), z++); print1(z, ", "); x = y; y = z; ); } \\ Michel Marcus, May 08 2016
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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