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A282432
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Number of primes of the form n - 3^k.
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3
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0, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 0, 1, 0, 3, 0, 2, 0, 1, 0, 2, 0, 1, 1, 2, 0, 4, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 1, 2, 0, 3, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 0, 4, 0, 3, 0, 1, 0, 3, 0
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OFFSET
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1,6
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LINKS
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FORMULA
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G.f.: ( Sum_{i>=0} x^(3^i) ) * ( Sum_{j>=1} x^prime(j) ). - Ilya Gutkovskiy, Feb 10 2022
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EXAMPLE
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a(14) = 3; 14 - 3^0 = 13, 14 - 3 = 11, 14 - 3^2 = 5, three primes.
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MAPLE
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a := 0 ;
for k from 0 do
if n-3^k < 2 then
return a ;
elif isprime(n-3^k) then
a := a+1 ;
end if;
end do:
end proc:
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PROG
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(Magma) lst:=[]; for n in [1..105] do c:=0; e:=Floor(Log(3, n)); k:=0; while k le e do p:=n-3^k; if IsPrime(p) then c+:=1; end if; k+:=1; end while; Append(~lst, c); end for; lst;
(PARI) ispp3(n) = (n==1) || (n==3) || (ispower(n, , &p) && (p==3));
a(n) = {my(nb = 0); forprime(p=2, n, nb += ispp3(n-p); ); nb; } \\ Michel Marcus, Feb 18 2017
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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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STATUS
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approved
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