A137995 Nearest integer to 1/frac(Pi^A137994(n)), where frac(x) = x - floor(x).

7, 159, 270, 308, 745, 758, 796, 1080, 1227, 7805, 13876, 62099, 70718, 86902, 154756

Offset: 1

Author

M. F. Hasler, inspired by Leroy Quet, Apr 05 2008

Keywords

• nonn
• more

Comments

Sequence A137994 could be defined as "least positive integer such that this one (without rounding) is increasing".

The term a(1)=7 is not surprising (3 + 1/7 = 3.14...) but it comes as a funny surprise that the next term, a(2)=159, matches the next 3 digits of Pi and a(3) just differs by 5 from the next 3 digits!

Crossrefs

Cf. A137994, A001203, A001672, A137299, A138324.

Programs

PARI

default(realprecision,10^4); f=1; for(i=1,10^9, frac(Pi^i)
				

Extensions

a(7) inserted and a(11)-a(15) added by Amiram Eldar, Jun 28 2025