A236686 - OEIS

A236686

Possible values for positive integers a,b,c,d such that 1/a + 1/b + 1/c + 1/d = 1.

2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 24, 42

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A236681 and the link for further motivation.

LINKS

Table of n, a(n) for n=1..15.

J. Baez, 42, May 25, 2013.

EXAMPLE

The solutions [a,b,c,d] of 1/a + 1/b + 1/c + 1/d = 1 are, in lexicographical order: {[2, 3, 7, 42], [2, 3, 8, 24], [2, 3, 9, 18], [2, 3, 10, 15], [2, 3, 12, 12], [2, 4, 5, 20], [2, 4, 6, 12], [2, 4, 8, 8], [2, 5, 5, 10], [2, 6, 6, 6], [3, 3, 4, 12], [3, 3, 6, 6], [3, 4, 4, 6], [4, 4, 4, 4]}.

PROG

(PARI) a=[]; forvec(v=vector(3, i, [2, 99]), numerator(s=sum(j=1, 3, 1/v[j], -1))==-1&&a=setunion(a, Set(v)), 1); a

(PARI) /* to display the solutions */ forvec(v=vector(3, i, [2, 99]), numerator(s=sum(j=1, 3, 1/v[j], -1))==-1&&-1/s>=v[3]&&print1(concat(v, -1/s), ", "), 1)

CROSSREFS

Cf. A236681, A236682, A236683, A236684.

Sequence in context: A133184 A102576 A101170 * A246084 A260768 A130224

Adjacent sequences: A236683 A236684 A236685 * A236687 A236688 A236689

KEYWORD

nonn,fini,full

AUTHOR

M. F. Hasler, Jan 29 2014

STATUS

approved