A327755 Odd integers k such that binomial(k-1,(k-1)/2) is coprime to k.

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 55, 57, 59, 61, 65, 67, 71, 73, 75, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133, 137, 139, 149, 151, 157, 163, 167, 169, 171, 173, 179, 181, 183, 191, 193, 197, 199

Offset

1,2

Comments

Integer k is in this sequence if for every prime p|k, the base-p representation of (k-1)/2 is composed of digits not exceeding (p-1)/2.

Contains all odd primes. Composite terms are listed in A327756.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms of Harvey P. Dale)

Example

21 is in the sequence because it is odd and binomial(20 - 1, (20 - 1)/2) = 2^2 * 11 * 13 * 17 * 19 which is coprime 3 * 7. - David A. Corneth, Mar 09 2024

Mathematica

Select[Range[1, 401, 2], CoprimeQ[#, Binomial[#-1, (#-1)/2]]&] (* Harvey P. Dale, Feb 25 2024 *)

Prog

(PARI) is(n) = {
	if(!bitand(n, 1), return(0));
	my(f = factor(n), h = (n-1)/2, v);
	for(i = 1, #f~,
		v = val(n-1, f[i, 1]) - 2*val(h, f[i, 1]); 	
		if(v > 0,
			return(0)
		)
	); 1
}
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Mar 09 2024

Crossrefs

Cf. A327756.

Sequence in context: A366251 A336620 A318978 * A322903 A363691 A349174

Adjacent sequences: A327752 A327753 A327754 * A327756 A327757 A327758

Keyword

nonn

Author

Max Alekseyev, Sep 24 2019

Status

approved