A021733 -id:A021733 - cp's OEIS frontend

A021247 Decimal expansion of 1/243.

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

Offset: 0

N. J. A. Sloane, Dec 11 1996

Period 27 Repeat: [0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9, 6, 7, 0, 7, 8, 1, 8, 9, 3]. - Wesley Ivan Hurt, May 25 2014

			0.00411522633744855967078189300411522633744855967078189300411522633744855967078...

Eric Weisstein's World of Mathematics, 243.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A010701 (1/3), A000012 (1/3^2), A021085 (1/3^4), A021733 (1/3^6).

Cf. A068542 (period of the fraction 1/3^n).

Digits:=100; evalf(1/243); # Wesley Ivan Hurt, May 25 2014

RealDigits[1/243, 10, 100, -1][[1]] (* Wesley Ivan Hurt, May 25 2014; corrected by Harvey P. Dale, Jan 23 2019 *)
PadRight[{},120,{0,0,4,1,1,5,2,2,6,3,3,7,4,4,8,5,5,9,6,7,0,7,8,1,8,9,3}] (* Harvey P. Dale, Jan 23 2019 *)

A021247_upto(N=100)={localprec(N+3);digits((1/3^5+1)\.1^N)[^1]} \\ M. F. Hasler, Apr 23 2021

1/243 = 1/3^5. - M. F. Hasler, Apr 23 2021

A343616 Decimal expansion of P_{3,2}(6) = Sum 1/p^6 over primes == 2 (mod 3).

Original entry on oeis.org

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

Offset: 0

M. F. Hasler, Apr 25 2021

The prime zeta modulo function P_{m,r}(s) = Sum_{primes p == r (mod m)} 1/p^s generalizes the prime zeta function P(s) = Sum_{primes p} 1/p^s.

			0.015689614727130461563527666152209091814208675553077763366153188676457...

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, value P(m=3, n=2, s=6), p. 21.
OEIS index to entries related to the (prime) zeta function.

Cf. A003627 (primes 3k-1), A001014 (n^6), A085966 (PrimeZeta(6)), A021733 (1/3^6).
Cf. A343612 - A343619 (P_{3,2}(s): analog for 1/p^s, s = 2 .. 9).
Cf. A343626 (for primes 3k+1), A086036 (for primes 4k+1), A085995 (for primes 4k+3).

A343616_upto(N=100)={localprec(N+5); digits((PrimeZeta32(6)+1)\.1^N)[^1]} \\ see A343612 for the function PrimeZeta32

P_{3,2}(6) = Sum_{p in A003627} 1/p^6 = P(6) - 1/3^6 - P_{3,1}(6).

A384917 Decimal expansion of 1/3645.

Original entry on oeis.org

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

Offset: 0

Davide Rotondo, Jun 12 2025

			0.0002743484224965706447187928669410...

Cf. A002378, A021733.

RealDigits[1/3645, 10, 120, -1][[1]] (* Amiram Eldar, Jun 12 2025 *)

Equals Sum_{k>=1} (k*(k+1))/10^(k+3).

Equals A021733/5. - Hugo Pfoertner, Jun 12 2025

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A021247 Decimal expansion of 1/243.

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A343616 Decimal expansion of P_{3,2}(6) = Sum 1/p^6 over primes == 2 (mod 3).

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A384917 Decimal expansion of 1/3645.

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