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A101264
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a(n) = 1 if 2*n + 1 is prime, otherwise a(n) = 0.
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20
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0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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Inverse Mobius transform of the sequence, after dropping a(0), yields A086668. - R. J. Mathar, Jan 25 2009
If we drop a(0) then we may describe the sequence as: for all numbers k(n) [k(n) = 4 ceiling(n/2) + (-1)^n] congruent to -1 or +1 (mod 4) starting with k(n) = {3,5,7,9,11,...}, a(k(n)) is 1 if k(n) is prime and 0 if k(n) is composite. - Daniel Forgues, Mar 01 2009
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REFERENCES
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D. H. Lehmer, "Computer Technology Applied to the Theory of Numbers," from Studies in Number Theory, ed. William J. LeVeque. Englewood Cliffs, New Jersey: Prentice Hall (1969): 138.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1 because 2*1+1 = 3 is prime;
a(2) = 1 because 2*2+1 = 5 is prime;
a(3) = 1 because 2*3+1 = 7 is prime;
a(4) = 0 because 2*4+1 = 9 is composite.
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MAPLE
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with(numtheory): a:= proc(n) if isprime(2*n+1)=true then 1 else 0 fi end:
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MATHEMATICA
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Table[If[PrimeQ[2n + 1], 1, 0], {n, 0, 104}] (* Ray Chandler, Jan 09 2005 *)
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PROG
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(Magma) [IsPrime(2*n+1) select 1 else 0: n in [1..100]]; // Marius A. Burtea, Aug 25 2019
(PARI) first(n) = {my(res = vector(n)); forprime(p = 3, 2*n - 1, res[p \ 2] = 1); res} \\ David A. Corneth, Aug 25 2019
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CROSSREFS
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KEYWORD
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easy,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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