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 A021023 Decimal expansion of 1/19. 5
 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, 0, 5, 2, 6, 3, 1, 5, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The 18-digit cycle 1, 0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2 in this sequence and the others based on nineteenths gives the successive digits of the smallest integer which is doubled, quadrupled and octupled when the last three digits in turn are moved from the right hand end to the left hand end. For example, 842105263157894736 is eight times 105263157894736842. - Ian Duff, Jan 07 2009, Jan 12 2009 The magic square that uses the decimals of 1/19 is fully magic. 383 has the same property (see A021387). For other such primes see A072359. - Michel Marcus, Sep 02 2015 Since 19 is prime and the cycle of its reciprocal's base 10 digits is 19 - 1 long, 19 is a full reptend prime (A001913). - Alonso del Arte, Mar 21 2020 REFERENCES Martin Gardner, Cyclic numbers, Mathematical Circus, Chapter 10, p. 172, of the 1992 Mathematical Association of America edition. GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 92. LINKS Table of n, a(n) for n=0..98. Wikipedia, Prime reciprocal magic square Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,-1,1). FORMULA G.f.: -x*(x^8 + x^7 + 2*x^6 + 4*x^5 - 2*x^4 - 3*x^3 + 4*x^2 - 3*x + 5)/((x - 1)*(x + 1)*(x^2 - x + 1)*(x^6 - x^3 + 1)). - Colin Barker, Aug 15 2012 MATHEMATICA Prepend[First@ RealDigits[N[1/19, 120]], 0] (* Michael De Vlieger, Sep 02 2015 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {0, 5, 2, 6, 3, 1, 5, 7, 8, 9}, 100] (* or *) PadRight[{}, 100, {0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1}] (* Harvey P. Dale, Jan 23 2021 *) PROG (PARI) default(realprecision, 2000); 1/19.0 \\ Anders Hellström, Sep 02 2015 (Scala) def longDivRecip(n: Int, places: Int = 100): List[Int] = { val pow10 = Math.pow(10, Math.ceil(Math.log10(Math.abs(n)))).toInt val digits = new scala.collection.mutable.ListBuffer[Int]() var quotient = pow10; var remainder = 0 while (digits.size < places) { remainder = quotient % n; quotient /= n; digits += quotient quotient = remainder * 10 } digits.toList } 0 :: longDivRecip(19) // Alonso del Arte, Mar 20 2020 CROSSREFS Cf. A021387, A072359. Sequence in context: A018247 A152025 A021099 * A078716 A308081 A164103 Adjacent sequences: A021020 A021021 A021022 * A021024 A021025 A021026 KEYWORD nonn,cons,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified May 28 09:20 EDT 2023. Contains 362999 sequences. (Running on oeis4.)