A071997 a(n) is the smallest positive integer that cannot be obtained by using the number 2 at most n times and the operators +, -, *, /.

1, 3, 5, 7, 11, 19, 27, 43, 75, 115, 171, 307, 555, 691, 1383, 2467, 3627, 7243, 10995, 17587, 28973, 57943, 87963, 151133, 267573, 465293, 807629, 1407093, 2390667, 4216531, 7122293, 11245133, 21756267, 39652589

Offset

1,2

Links

Table of n, a(n) for n=1..34.

G. Bannay, Countdown Problem

Austin T. Mohr, Recursive Python implementation

Example

a(3)=5 because using 2 at most thrice we can get 2/2=1, 2=2, 2+(2/2)=3, 2+2=4, but we cannot obtain 5 in the same way.

Crossrefs

Cf. A048175.

Sequence in context: A382685 A362250 A161420 * A093442 A364920 A155008

Adjacent sequences: A071994 A071995 A071996 * A071998 A071999 A072000

Keyword

nonn,hard,more

Author

Koksal Karakus (karakusk(AT)hotmail.com), Jun 17 2002

Extensions

a(18)-a(34) from Austin T. Mohr, May 17 2021

Corrected a(24) = 136627 to a(24) = 151133, since 136627 = 317*431 = (2/2+2*(2*2*2*2*(2+2*2*2)-2))*(2*2*(2+2*2)*(2+2*2*2*2)-2/2) from Andrej Jakobcic, Nov 02 2025

Status

approved