A395995 - OEIS

A395995

Smallest number k in 1..n such that GCD(n,k) = 1 and the greedy Egyptian fraction representation of k/n has more terms than the shortest representation of k/n as a sum of unit fractions; or 0 if no such k exists.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 14, 9, 5, 0, 7, 0, 3, 0, 0, 11, 9, 0, 5, 5, 7, 25, 16, 0, 9, 9, 29, 13, 4, 13, 7, 0, 7, 15, 9, 11, 4, 7, 5, 5, 13, 0, 3, 11, 32, 25, 8, 0, 5, 29, 5, 29, 4, 47, 8, 15, 11, 17, 7, 7, 4, 23, 7, 17, 4, 19, 11

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OFFSET

1,17

LINKS

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Egyptian fractions.

FORMULA

a(n) = 0 if and only if n is in A396000.

a(n) = 3 if and only if n is in A395997.

EXAMPLE

For n = 17, 4/17 is the only fraction for which the greedy Egyptian fraction representation has more terms than the shortest representation, so a(17) = 4.

For n = 42 there are 2 such fractions, 13/42 and 31/42, so a(42) = 13. For the smaller fraction 10/42 = 5/21, the greedy Egyptian fraction representation also has more terms than the shortest representation, but since 10 and 42 have a common factor it is discarded.

CROSSREFS

Cf. A050205, A097847, A395994, A395996, A395997, A395998, A395999, A396000, A396001.

Sequence in context: A117788 A233398 A006710 * A141150 A081162 A095367

Adjacent sequences: A395991 A395993 A395994 * A395996 A395997 A395998

KEYWORD

nonn,new

AUTHOR

Pontus von Brömssen, May 14 2026

STATUS

approved