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A092111
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a(n) = n+1 minus the greatest number of 1's in the binary representations of primes between 2^n and 2^(n+1).
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2
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0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,14
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COMMENTS
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0's occur only at Mersenne prime exponents (A000043) - 1, twos are in A092112, threes do not appear < 504.
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LINKS
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FORMULA
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MAPLE
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f:= proc(n) local t, j, k;
t:= 2^(n+1)-1;
if isprime(t) then return 0 fi;
for j from 1 to n-1 do if isprime(t-2^j) then return 1 fi od;
for j from 1 to n-2 do for k from j+1 to n-1 do
if isprime(t-2^j-2^k) then return 2 fi od od;
FAIL
end proc:
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MATHEMATICA
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Compute the second line of the Mathematica code for A091938, then (Table[n + 1, {n, 105}]) - (Count[ IntegerDigits[ #, 2], 1] & /@ Table[ f[n], {n, 105}])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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