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 A092111 a(n) = n+1 minus the greatest number of 1's in the binary representations of primes between 2^n and 2^(n+1). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 COMMENTS 0's occur only at Mersenne prime exponents (A000043) - 1, twos are in A092112, threes do not appear < 504. a(n) <= 2 for n <= 2000. - Robert Israel, Mar 05 2020 LINKS Robert Israel, Table of n, a(n) for n = 1..2000 FORMULA a(n) = n+1 - A091937(n). MAPLE 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: map(f, [\$1..200]); # Robert Israel, Mar 05 2020 MATHEMATICA 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}]) CROSSREFS Cf. A091938, A092112. Sequence in context: A330262 A098055 A344739 * A330167 A307776 A341027 Adjacent sequences:  A092108 A092109 A092110 * A092112 A092113 A092114 KEYWORD nonn AUTHOR Robert G. Wilson v, Feb 20 2004 STATUS approved

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)