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A361180
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Primes p such that the odd part of p - 1 is upper-bounded by the dyadic valuation of p - 1.
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1
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3, 5, 17, 97, 193, 257, 641, 769, 12289, 18433, 40961, 65537, 114689, 147457, 163841, 786433, 1179649, 5767169, 7340033, 13631489, 23068673, 167772161, 469762049, 2013265921, 2281701377, 3221225473, 3489660929, 12348030977, 77309411329, 206158430209, 2061584302081, 2748779069441
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OFFSET
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1,1
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COMMENTS
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Primes of the form k*2^m + 1 where k <= m and k is odd. - David A. Corneth, Mar 03 2023
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LINKS
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EXAMPLE
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3 is a term because the odd part of 2 is 1, the dyadic valuation of 2 is 1 and 1 <= 1.
641 = 5*2^7 + 1 is a term because the odd part of 640 is 5, the dyadic valuation of 640 is 7 and 5 <= 7.
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MAPLE
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aList := proc(upto)
local i, j, p, R:
R := {}:
for i from 1 to ilog2(upto) do
for j from 1 to min(i, floor(upto/2^i)) do
p := j*2^i+1:
if isprime(p) then R := `union`(R, {p}): fi: od: od:
R: end:
aList(10^12);
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PROG
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(PARI) isok(p) = if (isprime(p), my(m=valuation(p-1, 2)); (p-1)/2^m <= m); \\ Michel Marcus, Mar 03 2023
(PARI) upto(n) = {my(res = List()); for(i = 1, logint(n, 2), forstep(j = 1, min(i, n>>i), 2, if(isprime((j<<i) + 1), listput(res, (j<<i) + 1) ) ) ); Set(res) } \\ David A. Corneth, Mar 03 2023
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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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STATUS
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approved
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