A084925 Inverse hyperbolic cotangent irreducible numbers: positive integers such that the arccoth of these numbers form a basis for the space of arccoth of rationals >=1. The hyperbolic analog of the Stormer numbers (A005528).

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 58, 60, 62, 66, 68, 70, 72, 74, 78, 80, 82, 84, 88, 90, 92, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 122, 126, 128, 130, 132, 136, 138, 140, 142, 144, 148, 150

Offset

1,2

Comments

n is in the sequence if y = (xn+1)/(x+n) is noninteger for all integer x where 1 < x < n. Equivalently, n is in the sequence when n cannot be formed by (xy-1)/(x-y) for all integers x and y where x < n and 1 < y < x, so n cannot satisfy ((n+1)/(n-1))*((x+1)/(x-1)) = ((y+1)/(y-1)). Thus all the nearest neighbors of the primes (A045718) appear in this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paul D. Hanna)

Prog

(PARI) for(n=1, 150, x=1; b=0; while(x<n, x=x+1; r=(x+n)*floor((x*n+1)/(x+n)); if(r>=(x *n+1), b=b+1)); if(b<=0, print1(n, ", ")))

Crossrefs

Cf. A005528 (Stormer numbers), A045718, A084926.

Sequence in context: A333183 A068670 A371925 * A045718 A068005 A055721

Adjacent sequences: A084922 A084923 A084924 * A084926 A084927 A084928

Keyword

nonn

Author

Paul D. Hanna, Jun 12 2003

Status

approved