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 A177378 a(n) is the smallest prime p>2 such that there are 2*n or 2*n+1 positive integers m for which the exponents of 2 and p in the prime power factorization of m! are both powers of 2. 5
 11, 13, 3, 29, 31, 251, 127, 509, 1021, 4091, 4093, 65519, 8191, 131063, 262133, 262139, 131071, 1048571, 524287, 8388593, 4194301, 67108837, 16777213, 67108861, 1073741789, 2147483587, 2147483629, 536870909 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236. FORMULA For sufficiently large n, 2^n - 1 <= a(n) <= 2^ceiling(40*n/19). Let k >= n. Put g = g(n,k) = min{odd j >= 2^(k-n): 2^k - j is prime} and h(n) = min{k: k - n = floor(log_2(g))}. Then a(n) = 2^h(n) - g(n,h(n)). EXAMPLE By the formula, for n=6, consider k >= 6. If k=6, then g(6,6) = 3, but 6 does not equal to 6 - floor(log_2(3)); if k=7, then g=15, but 6 does not equal to 7 - floor(log_2(15)); if k=8, then g=5 and we see that 6 = 8 - floor(log_2(5)). Therefore a(6) = 2^8 - 5 = 251. CROSSREFS Cf. A000142, A050376, A169655, A169661, A177349, A177355, A177436, A177458, A177459, A177498. Sequence in context: A262282 A034080 A107805 * A110059 A004476 A112133 Adjacent sequences:  A177375 A177376 A177377 * A177379 A177380 A177381 KEYWORD nonn AUTHOR Vladimir Shevelev, May 07 2010 STATUS approved

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Last modified June 21 06:24 EDT 2021. Contains 345358 sequences. (Running on oeis4.)