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A071635
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Number of decompositions of 4*n+2 into sum of two primes of form 4*k+1.
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3
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0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 2, 3, 0, 3, 2, 2, 3, 2, 1, 3, 2, 1, 4, 3, 2, 5, 3, 2, 5, 3, 2, 3, 4, 2, 5, 4, 1, 5, 3, 3, 4, 4, 1, 6, 4, 3, 6, 5, 2, 9, 3, 3, 4, 4, 2, 6, 4, 2, 8, 4, 4, 5, 4, 3, 8, 5, 2, 7, 7, 4, 9, 6, 3, 7, 6, 3, 6, 6, 2, 12, 5, 4, 8, 6, 5, 10, 4, 2, 10, 7, 4
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OFFSET
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0,9
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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a(10)=2 as 4*10+2 = 42 = 5+37 = (4*1+1)+(4*9+1) = 13+29 = (4*3+1)+(4*7+1) and the other two decompositions 42 = 11+31 = (4*2+3)+(4*7+3) = 19+23 = (4*4+3)+(4*5+3), A002375(21)=4.
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MATHEMATICA
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a[n_] := Module[{s = 0}, For[p = 3, p <= 2n+1, p = NextPrime[p], If[Mod[p, 4] == 1 && PrimeQ[4n+2-p], s++]]; s];
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PROG
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(PARI) a(n)={my(s=0); forprime(p=3, 2*n+1, if(p%4==1 && isprime(4*n+2-p), s++)); s} \\ Andrew Howroyd, Feb 02 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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