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A092636
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Number of consecutive prime runs of 1 prime congruent to 1 mod 4 below 10^n.
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4
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1, 5, 31, 208, 1555, 12465, 102704, 869060, 7540342, 66571720, 595513442
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OFFSET
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1,2
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LINKS
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FORMULA
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Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just one prime occurs before interruption by a prime congruent to 3 mod 4.
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EXAMPLE
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a(3)=31 because 31 single primes occur below 10^3, each interrupted in the run by a prime congruent to 3 mod 4.
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MATHEMATICA
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A002144 = Select[4 Range[0, 10^4] + 1, PrimeQ[#] &];
A002145 = Select[4 Range[0, 10^4] + 3, PrimeQ[#] &];
lst = {}; Do[If[Length[s = Select[A002144, Between[{A002145[[i]], A002145[[i + 1]]}]]] == 1, AppendTo[lst, Last[s]]], {i, Length[A002145] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}] (* Robert Price, May 31 2019 *)
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PROG
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(PARI) a(n)=my(p=2, q=3, t); forprime(r=5, nextprime(10^n), if(q%4==1&&p%4==3&&r%4==3, t++); p=q; q=r); t \\ Charles R Greathouse IV, Sep 30 2011
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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