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A096447
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Odd primes p such that the number of primes less than p that are congruent to 1 (mod 4) is equal to the number of primes less than p that are congruent to 3 (mod 4).
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18
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3, 7, 19, 43, 463, 26839, 26861, 26879, 26891, 26903, 26927, 616783, 616799, 616841, 616849, 616877, 617039, 617269, 617369, 617401, 617429, 617453, 617471, 617479, 617521, 617537, 617587, 617689, 617717, 617723, 618439, 618547, 618619, 618643
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OFFSET
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1,1
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COMMENTS
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Assign the odd prime numbers to the rows of an array as follows:
Assign the first odd prime, prime(2) = 3, to row 0 (the top row).
For m > 2, assign prime(m) to the row immediately above or below the row to which prime(m-1) was assigned: above if prime(m-1) == 1 (mod 4), below otherwise.
The following array results:
row 0 (this sequence): 3, 7, 19, 43, 463, 26839, ...
row 1 (A096448): 5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ...
row 2 (A096451): 13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ...
row 3: 73, 83, 97, 109, ...
row 4: 89, ...
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LINKS
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FORMULA
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MATHEMATICA
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lim = 10^5; k1 = 0; k3 = 0; p = 2; t = {}; Do[p = NextPrime[p]; If[k1 == k3, AppendTo[t, p]]; If[Mod[p, 4] == 1, k1++, k3++], {lim}]; t (* T. D. Noe, Sep 07 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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