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A057775
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a(n) is the least prime p such that p-1 is divisible by 2^n and not by 2^(n+1).
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11
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2, 3, 5, 41, 17, 97, 193, 641, 257, 7681, 13313, 18433, 12289, 40961, 114689, 163841, 65537, 1179649, 786433, 5767169, 7340033, 23068673, 104857601, 377487361, 754974721, 167772161, 469762049, 2013265921, 3489660929, 12348030977, 3221225473, 75161927681
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OFFSET
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0,1
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COMMENTS
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If we drop the requirement that p-1 must not be divisible by 2^(n+1), we get instead A035089, which is a nondecreasing sequence. - Jeppe Stig Nielsen, Aug 09 2015
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LINKS
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EXAMPLE
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a(13) = 40961 = 1 + 8192*5 where the last term is divisible by the 13th power of 2 and 40961 is the smallest prime with that property.
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MAPLE
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f:= proc(n) local p;
for p from 2^n+1 by 2^(n+1) do
if isprime(p) then return p fi
od
end proc:
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MATHEMATICA
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Table[k = 1; While[p = k*2^n + 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}] (* T. D. Noe, Dec 27 2011 *)
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PROG
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(PARI) a(n)=forstep(k=1, 9e99, 2, isprime((k<<n)+1)&return((k<<n)+1)) \\ Jeppe Stig Nielsen, Aug 09 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000
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STATUS
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approved
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