A395834 Digits of the 10-adic integer x satisfying x = 1 + 10*x^2.

1, 1, 2, 5, 4, 3, 6, 2, 4, 9, 6, 5, 3, 6, 0, 2, 3, 6, 5, 2, 6, 0, 6, 0, 8, 8, 8, 8, 0, 7, 1, 7, 6, 4, 4, 5, 9, 2, 5, 4, 1, 0, 2, 9, 0, 2, 6, 3, 6, 3, 5, 5, 7, 9, 7, 5, 9, 8, 1, 5, 1, 2, 1, 7, 5, 5, 9, 7, 5, 3, 9, 0, 1, 0, 6, 2, 2, 8, 7, 5, 4, 8, 6, 8, 1, 5, 5, 3, 7, 9, 4, 6, 8, 7, 3, 9, 8, 8, 8, 2

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Formula

x = Sum_{n>=0} A000108(n)*10^n evaluated as a 10-adic integer sum.

Since 1/x = 10*x - 1 then 1/x = 9 + Sum_{n>=1} A000108(n)*10^n as a 10-adic integer sum.

Example

x = ...5536362092014529544671708888060625632063569426345211
where x = 1 + 10*x^2.
This constant equals the 10-adic sum involving the Catalan numbers:
x = 1 + 1*10 + 2*10^2 + 5*10^3 + 14*10^4 + 42*10^5 + 132*10^6 + 429*10^7 + ... + A000108(n)*10^n + ...
Also, x = (1 + y)/20 where a 10-adic integer value of y = -sqrt(-39) (y^2 = ...999999961) is y = ...727241840290590893434177761212512641271388526904219.
Also, the 10-adic integer value of -1/x = 10*x - 1 = ...256320635694263452109. Thus, x satisfies x * (10*x - 1) = ...999999999 = -1 (see A395839).

Prog

(PARI) \\ Displays N digits
upto(N) = {CAT = (1 - sqrt(1-4*x +x^2*O(x^(2*N))))/(2*x);
CAT10 = subst(truncate(CAT), x, 10);
DIGITS = Vecrev(digits(CAT10%(10^N)))}
upto(100)

Crossrefs

Cf. A395839, A018247, A120817, A000108.

Sequence in context: A184832 A111449 A210800 * A222235 A163332 A275105

Adjacent sequences: A395831 A395832 A395833 * A395835 A395836 A395837

Keyword

nonn,base

Author

Paul D. Hanna, May 11 2026

Status

approved