A361980 a(n) is the n-th decimal digit of p(n)/q(n) where p(n) = A002260(n) and q(n) = A004736(n).

1, 5, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 2, 3, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 6, 0, 0, 3, 0, 0, 0, 2, 0, 8, 3, 0, 0, 6, 0, 0, 0, 0, 3, 0, 8, 0, 0, 0, 0, 0, 0, 3, 1, 0, 4, 0, 4, 6, 0, 0, 3, 0, 0, 3, 6, 7, 0, 5, 0, 0, 3, 0, 0, 6, 0, 0, 5, 5, 0, 6, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 6

Offset: 1

Author

Jesiah Darnell, Apr 01 2023

Keywords

• base
• cons
• easy
• nonn

Comments

Decimal digit positions are numbered 1 for the units, 2 for immediately after the decimal point, and so on.

This sequence can be interpreted as the decimal digits of a constant 1.5030006...

This constant shares an infinite number of decimal digits with any given rational r. This is since p,q go through all pairs of integers >= 1 and so p(n)/q(n) = r for infinitely many n.

This constant is irrational.

Examples

			p(1) = 1, q(1) = 1, p/q = 1/1 = 1,  a(1) = 1.
p(2) = 1, q(2) = 2, p/q = 1/2 = 0.5, a(2) = 5.
p(3) = 2, q(3) = 1, p/q = 2/1 = 2.00, a(3) = 0.
p(4) = 1, q(4) = 3, p/q = 1/3 = 0.333..., a(4) = 3.
		

Crossrefs

Cf. A002260, A004736, A061480.

Programs

PARI

p(n) = n-binomial(floor(1/2+sqrt(2*n)), 2); \\ A002260
q(n) = binomial( floor(3/2 + sqrt(2*n)), 2) - n + 1; \\ A004736
a(n) = my(r = p(n)/q(n)); floor(r*10^(n-1)) % 10; \\ Michel Marcus, Apr 05 2023