A064395 Primes p for which the exponent of the highest power of 2 dividing p! is equal to prevprime(p).

5, 23, 71, 83, 101, 113, 197, 281, 353, 359, 373, 401, 599, 683, 739, 751, 773, 977, 1091, 1097, 1103, 1217, 1223, 1229, 1237, 1283, 1553, 1559, 1601, 1607, 1619, 2039, 2347, 2357, 2389, 2417, 2473, 2539, 2671, 2699, 2749, 2857, 3019, 3049, 3499, 3581

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 400 terms from Harvey P. Dale)

Formula

{ A000040 } intersect { A064394 }. - Alois P. Heinz, Jul 10 2022

Example

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.

Maple

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:

Mathematica

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} ]
Select[Partition[Prime[Range[510]], 2, 1], IntegerExponent[#[[2]]!, 2] == #[[1]]&] [[All, 2]] (* Harvey P. Dale, Feb 22 2018 *)

Crossrefs

Complement of A064393 relative to A064394.

Cf. A000040.

Sequence in context: A284648 A290187 A243442 * A230497 A138905 A125955

Adjacent sequences: A064392 A064393 A064394 * A064396 A064397 A064398

Keyword

nonn

Author

Vladeta Jovovic, Sep 29 2001

Extensions

More terms from James A. Sellers, Oct 01 2001

Status

approved