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A240504
Read (exponents of primes in the factorization of n!) modulo 2 and convert to decimal.
3
1, 3, 3, 7, 1, 3, 11, 11, 1, 3, 11, 23, 51, 43, 43, 87, 23, 47, 15, 95, 215, 431, 47, 47, 295, 423, 391, 783, 143, 287, 1311, 1887, 847, 719, 719, 1439, 3471, 2511, 975, 1951, 7583, 15167, 14655, 12607, 4383, 8767, 575, 575, 16959, 25407, 24895, 49791, 639, 10879
OFFSET
2,2
LINKS
EXAMPLE
Since 9! = 2^7*3^4*5*7, then we have a binary number the digits of which are the exponents modulo 2: 1011. In decimal this is 11. So a(9)=11.
PROG
(PARI) a(n) = subst(Pol(factor(n!)[, 2] % 2), x, 2); \\ Michel Marcus, Feb 15 2016
(PARI) a(n) = { my(res = 0); forprime(p = 2, n, res = 2*res + (val(n, p)%2) ); res }
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Feb 24 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Apr 06 2014
EXTENSIONS
More terms from Michel Marcus, Feb 15 2016
STATUS
approved