A240504 Read (exponents of primes in the factorization of n!) modulo 2 and convert to decimal.

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

David A. Corneth, Table of n, a(n) for n = 2..10000

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

Cf. A055204, A240502, A336510.

Sequence in context: A261295 A118031 A335726 * A338775 A359407 A358191

Adjacent sequences: A240501 A240502 A240503 * A240505 A240506 A240507

Keyword

nonn,base

Author

Vladimir Shevelev, Apr 06 2014

Extensions

More terms from Michel Marcus, Feb 15 2016

Status

approved