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%I #11 Jul 10 2022 17:45:29
%S 5,23,71,83,101,113,197,281,353,359,373,401,599,683,739,751,773,977,
%T 1091,1097,1103,1217,1223,1229,1237,1283,1553,1559,1601,1607,1619,
%U 2039,2347,2357,2389,2417,2473,2539,2671,2699,2749,2857,3019,3049,3499,3581
%N Primes p for which the exponent of the highest power of 2 dividing p! is equal to prevprime(p).
%H Alois P. Heinz, <a href="/A064395/b064395.txt">Table of n, a(n) for n = 1..10000</a> (first 400 terms from Harvey P. Dale)
%F { A000040 } intersect { A064394 }. - _Alois P. Heinz_, Jul 10 2022
%e 5!=2^3 * 3 * 5, 23!=2^19 * 3^9 * 5^4 * 7^3 * 11^2 * 13 * 17 * 19 * 23, 71!=2^67 * 3^32 * 5^16 * 7^11 * 11^6 * 13^5 * 17^4 * 19^3 * 23^3 * 29^2 * 31^2 * 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71.
%p for n from 3 to 10^4 do if sum(floor(n/(2^i)), i=1..15) = prevprime(n) and isprime(n) then printf(`%d,`,n) fi; od:
%t f[n_] := (t = 0; p = 2; While[s = Floor[n/p]; t = t + s; s > 0, p *= 2]; t); Do[ If[ f[Prime[n]] == Prime[n - 1], Print[ Prime[n]]], {n, 2, 10^3} ]
%t Select[Partition[Prime[Range[510]],2,1],IntegerExponent[#[[2]]!,2] == #[[1]]&] [[All,2]] (* _Harvey P. Dale_, Feb 22 2018 *)
%Y Complement of A064393 relative to A064394.
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Vladeta Jovovic_, Sep 29 2001
%E More terms from _James A. Sellers_, Oct 01 2001
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