cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A242833 Primes formed by the initial digits of the decimal expansion of 1/19, starting at the first nonzero digit in the expansion.

Original entry on oeis.org

5, 52631, 5263157894736842105263157, 52631578947368421052631578947368421052631578947368421052631
Offset: 1

Views

Author

Felix Fröhlich, May 23 2014

Keywords

Comments

a(5) has 95 digits and a(6) has 907 digits. - Michel Marcus, May 27 2014

Links

Crossrefs

Cf. A021023.
Corresponding sequences for 1/k: A242824 (k=7), A093676 (k=12), A242826 (k=13), A242827(k=14), A242828 (k=17).

Programs

  • PARI
    lista(nn) = {v = [5,2,6,3,1,5,7,8,9,4,7,3,6,8,4,2,1,0]; n = 0; for (i=0, nn, n = 10*n+ v[(i % 18)+1]; if (ispseudoprime(n), print1(n, ", ")););} \\ Michel Marcus, May 27 2014

A072359 Primes p such that the p-1 digits of the decimal expansion of k/p (for k=1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.

Original entry on oeis.org

19, 383, 32327, 34061, 45341, 61967, 65699, 117541, 158771, 405817, 444287, 456503, 695389, 724781, 1102567, 1177859, 1498139, 2336989, 2695337, 3036857, 3249419, 3512749, 3571429, 4427299, 5141051, 7033823, 8324411, 9932179
Offset: 1

Views

Author

Lekraj Beedassy, Jul 18 2002

Keywords

References

  • W. S. Andrews, Magic Squares and Cubes, pp. 176 Dover NY 1960.
  • J. Heleen, Journal of Recreational Mathematics, 30(1) 1999-2000 pp. 72-3 Soln. to Prob. 2394. Magic Reciprocals
  • M. J. Zerger, Journal of Recreational Mathematics, 30(2) 1999-2000 pp. 158-160 Soln. to Prob. 2420. Only 19?

Links

Crossrefs

Cf. A021023 (1/19), A021387 (1/383), A096339, A096660.

Extensions

More terms from William Rex Marshall, Aug 18 2005

A321218 Decimal expansion of number of Pascals (Pa) in 1 Torr.

Original entry on oeis.org

1, 3, 3, 3, 2, 2, 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
Offset: 3

Views

Author

Jianing Song, Oct 31 2018

Keywords

Comments

1 Torr is defined to be exactly 1/760 of standard atmospheric pressure (101325 Pa), which is about 133.322368421052... Pa. Note that 1 Torr is slightly different from 1 mmHg (millimeter of mercury), which is defined to be exactly 133.322387415 Pa, or 13.5951 mmH2O (millimeters of water), with relative difference less than 0.000015%.
Period 18 from a(9) on.

Examples

			1 Torr = 1/760 atm = 101325/760 Pa = 20265/152 Pa.

Links

Crossrefs

Cf. A021023. A213611.

Programs

  • PARI
    default(realprecision, 100); 20265.0/152.0
  • PARI
    x='x+O('x^50); Vec(-x^3*(5*x^15-3*x^14+4*x^13-x^12-x^11-3*x^9+2*x^8+3*x^7+x^6-x^4+2*x+1)/((x-1)*(x+1)*(x^2-x+1)*(x^6-x^3+1)))

Formula

a(n) = A021023(n+3) for n >= 9.
G.f.: -x^3*(5*x^15 - 3*x^14 + 4*x^13 - x^12 - x^11 - 3*x^9 + 2*x^8 + 3*x^7 + x^6 - x^4 + 2*x + 1)/((x - 1)*(x + 1)*(x^2 - x + 1)*(x^6 - x^3 + 1))

A021387 Decimal expansion of 1/383.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

The magic square that uses the decimals of 1/383 is fully magic. 19 has the same property (see A021023). For other such primes see A072359. - Michel Marcus, Sep 02 2015

Links

Crossrefs

Cf. A021023, A072359.

Programs

  • Mathematica
    x = RealDigits[N[1/383, 120]]; Table[0, {Abs@ Last@ x}]~Join~First@ x (* Michael De Vlieger, Sep 02 2015 *)
realDigitsRecip[383] (* The realDigitsRecip program is at A021200 *) (* Harvey P. Dale, Aug 07 2025 *)
  • PARI
    default(realprecision,2000);1/383.0 \\ Anders Hellström, Sep 02 2015

A021042 Decimal expansion of 1/38.

Original entry on oeis.org

0, 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, 9
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

The probability of winning in American Roulette is 1/2 - 1/38 = 0.473684210526315789... - Jean-François Alcover, Jul 31 2019

Links

Crossrefs

Same period as A021023.

A254065 Vulgar fractions whose denominators are numbers ending with nine, the case 1/19.

Original entry on oeis.org

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

Views

Author

Gary W. Adamson, Jan 24 2015

Keywords

Comments

The method provides an alternative for obtaining reversals of decimal expansions of 1/n, where n is of the form 10x + 9. We then access the reversal of the periodic sequence, noting that it matches the decimal expansion of 1/19 as shown in A021023: (.0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1, ...). Page 23 of "Vedic Mathematics" states "In accordance with the sutra, we multiply it by 2" [since we have deleted the rightmost 9 and enhanced the remaining digit (a 1) by 1 = 2]. Then N. Ramamurthy states: "Similarly the multiplier for 49 is 5, for 149 is 15, for 12789 is 1279 and so on."

Examples

			Let 1/n = 1/19. Delete the 9 and increment the previous digit (1) by 1 to get 2, our multiplier M. Let the first term be 1, then continue multiplying by M, getting 1, 2, 4, 8, ... then the next term is 6 with a carryover of 1, giving (1, 2, 4, 8, 6, ...). The next term is 3 since 2 * 6 = 12; thus we mark down 3 (2 plus the carryover). The next term is 7 (being 2 * 3 plus the carryover of 1); proceeding in this way, we get 1, 2, 4, 8, 6, 3, 7, 4, 9, 8, 7, ...

References

  • L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 172.
  • N. Ramamurthy, "Vedic Mathematics, 30 Formulae Elucidated With Simple Examples", 9789382237273, published by N. Ramamurthy, http://ramamurthy.jaagruti.co.in, 2013, pp. 21-22.

Links

Crossrefs

Cf. A021023.

Formula

Given 1/n, where n ends in 9, delete the 9 and use the previous set of digits (incremented by 1) as a multiplier M; let the first term = 1. Perform M * 1 and carry over the remainder if any, marking down the result. Perform M * result, adding the carryover for the next operation, and continue until the sequence repeats.
G.f.: -x*(1+x+2*x^2+4*x^3-2*x^4-3*x^5+4*x^6-3*x^7+5*x^8) / ( (x-1) *(1+x) *(x^2-x+1) *(x^6-x^3+1) ). - R. J. Mathar, May 24 2016
a(n) = (2^(n-1) mod 19) mod 10. - Ridouane Oudra, Jan 16 2023

Extensions

Edited by Jon E. Schoenfield, Jan 16 2023
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.