A346603 The first of four solutions to a Monthly problem asking if there exist finite sequences 1 < a(1) < a(2) < ... < a(n) such that Sum_i 1/a(i) = 1 and gcd(a(i), a(i+1)) = 1 for 1 <= i < n.

3, 4, 5, 9, 22, 25, 99, 100

Offset

1,1

Comments

There are probably a large number of such sequences, but it seems worthwhile putting these four examples on record. They were the only solutions submitted.

Links

Table of n, a(n) for n=1..8.

Daniel Ullman, Proposer, Problem E3359, Amer. Math. Monthly, 98:2 (1991), 168.

Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A346604, A346605, A346606.

Sequence in context: A215176 A063781 A257041 * A056797 A029727 A086186

Adjacent sequences: A346600 A346601 A346602 * A346604 A346605 A346606

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Aug 06 2021

Status

approved