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A078687
Number of x>=0 such that prime(n)-2^x is prime.
6
0, 1, 1, 2, 2, 2, 1, 3, 2, 1, 2, 2, 1, 2, 2, 1, 1, 3, 2, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 0, 3, 1, 4, 0, 2, 2, 1, 3, 2, 1, 4, 1, 1, 2, 4, 2, 1, 3, 3, 1, 1, 3, 0, 2, 2, 1, 3, 2, 1, 2, 3, 1, 1, 2, 2, 0, 0, 2, 2, 3, 1, 2, 0, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 0, 1, 3, 2, 1, 1, 3, 1, 4
OFFSET
1,4
FORMULA
a(A049084(A065381(n)))=0, a(A049084(A065380(n)))=1; A118953(n)<=a(n); a(n)=A109925(A000040(n)). - Reinhard Zumkeller, May 07 2006
EXAMPLE
prime(17)=59 and only 59-2^3 = 53 is prime hence a(17)=1
MATHEMATICA
f[p_] := Block[{c = exp = 0, lmt = 1 + Floor@ Log2@ p}, While[exp < lmt, If[ PrimeQ[p - 2^exp], c++]; exp++]; c]; Array[ f@ Prime@# &, 105] (* Robert G. Wilson v, Jul 07 2014 *)
PROG
(PARI) a(n)=sum(i=0, floor(log(prime(n))/log(2)), if(isprime(prime(n)-2^i), 1, 0))
CROSSREFS
Cf. A156695.
Sequence in context: A230243 A338898 A376115 * A133138 A348193 A194326
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Dec 17 2002
STATUS
approved