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%I #12 Mar 14 2018 03:54:17
%S 317,467,619,1303,1307,1429,1433,1489,1613,1699,1873,2713,2719,2797,
%T 2971,3307,3541,3769,4937,5087,5233,5443,5479,5507,5527,5653,5657,
%U 5749,6047,6143,6571,7487,7547,7583,8017,8431,8867,9007,9931
%N Primes p for which the exponent of the highest power of 2 dividing p! is equal to prevprime(prevprime(p)).
%H Robert Israel, <a href="/A064396/b064396.txt">Table of n, a(n) for n = 1..10000</a>
%e 317!=2^311 * 3^155 * 5^77 * 7^51 * 11^30 * 13^25 * 17^19 * 19^16 * 23^13 * 29^10 * 31^10 * 37^8 * 41^7 * 43^7 * 47^6 * 53^5 * 59^5 * 61^5 * 67^4 * 71^4 * 73^4 * 79^4 * 83^3 * 89^3 * 97^3 * 101^3 * 103^3 * 107^2 * 109^2 * 113^2 * 127^2 * 131^2 * 137^2 * 139^2 * 149^2 * 151^2 * 157^2 * 163 * 167 * 173 * 179 * 181 * 191 * 193 * 197 * 199 * 211 * 223 * 227 * 229 * 233 * 239 * 241 * 251 * 257 * 263 * 269 * 271 * 277 * 281 * 283 * 293 * 307 * 311 * 313 * 317.
%p r:= 1: q:= 2: p:= 3: count:= 0: Res:= NULL:
%p while count < 100 do
%p r:= q; q:= p; p:= nextprime(p);
%p if add(floor(p/2^i),i=1..ilog2(p)) = r
%p then count:= count+1; Res:= Res, p;
%p fi
%p od:
%p Res; # _Robert Israel_, Mar 14 2018
%o (PARI) isok(p) = (precprime(precprime(p-1)-1) == factor(p!)[1, 2]) \\ _Michel Marcus_, Jun 17 2013
%K nonn
%O 1,1
%A _Vladeta Jovovic_, Sep 29 2001
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