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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 analogue of the Stormer numbers (A005528). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n is in the sequence if y=(xn+1)/(x+n) is non-integer for all integer x where 1<x<n. Equivalently, n is in the sequence when n can not be formed by (xy-1)/(x-y) for all integers x and y where x<n and 1<y<x; so that n can not 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

Table of n, a(n) for n=1..64.

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: A004271 A004278 A068670 * A045718 A068005 A055721

Adjacent sequences:  A084922 A084923 A084924 * A084926 A084927 A084928

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 12 2003

STATUS

approved

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Last modified October 24 04:24 EDT 2014. Contains 248497 sequences.