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.

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A333828 The 20-adic integer x = ...70D9AE7F1DI8 satisfying x^5 = x.

Original entry on oeis.org

8, 18, 13, 1, 15, 7, 14, 10, 9, 13, 0, 7, 6, 6, 13, 5, 14, 16, 0, 4, 11, 8, 8, 10, 8, 8, 3, 12, 6, 7, 19, 8, 10, 12, 11, 1, 1, 15, 2, 12, 8, 8, 10, 19, 4, 10, 19, 7, 17, 8, 12, 14, 9, 19, 11, 18, 16, 14, 19, 9, 4, 2, 16, 11, 0, 12, 11, 1, 6, 11, 12, 3, 3, 16, 11
Offset: 0

Views

Author

Patrick A. Thomas, Apr 07 2020

Keywords

Comments

Letters A through J represent the base-20 digits 10 through 19, respectively.
Conjecture: There exists a nontrivial n-adic integer x satisfying x^5 = x, and x^2, x^3, and x^4 are not x, if and only if n has a prime factor of the form 4k+1. Further, there is one nontrivial pair (x and -x) for each different prime factor of the form 4k+1.

Examples

			8^25 in base 20 ends in the digits 13, 18, 8 (or ...DI8 in extended hexadecimal notation).

Links

Crossrefs

Cf. A120817, A210850, A331548.

Formula

The last n+1 digits of 8^(5^n) in base 20, for all n.

A051276 Nonzero coefficients in one of the 5-adic expansions of sqrt(-1).

Original entry on oeis.org

2, 1, 2, 1, 3, 4, 2, 3, 3, 2, 2, 4, 1, 3, 2, 4, 4, 3, 4, 4, 1, 2, 4, 1, 4, 1, 1, 3, 1, 4, 1, 4, 2, 1, 1, 3, 3, 2, 2, 4, 4, 2, 4, 3, 1, 2, 4, 3, 3, 3, 3, 1, 3, 1, 1, 3, 3, 4, 1, 3, 3, 3, 4, 2, 2, 2, 1, 4, 1, 1, 4, 4, 2, 1, 2, 3, 4, 4, 4, 2, 2, 1, 3, 1, 3, 2, 4, 2, 1, 4, 3, 4, 3, 1, 2, 1, 3, 3, 3, 1, 1, 3, 1, 2, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			2 + 1*5 + 2*5^2 + 1*5^3 + 3*5^4 + 4*5^5 + 2*5^6 + 3*5^7 + 3*5^9 + 2*5^10 + 2*5^11 + 4*5^13 + 1*5^14 + 3*5^15 + 2*5^16 + 4*5^17 + 4*5^19 + ...

References

  • Kurt Mahler, Introduction to p-adic numbers and their functions. Cambridge Tracts in Mathematics, 76. Cambridge University Press, Cambridge-New York, 1971. See pp. 35ff.

Crossrefs

Cf. A034935, A048898, A048899, A210850, A210851.

Programs

  • Maple
    R:= select(t -> padic:-ratvaluep(t,1)=2,[padic:-rootp(x^2+1,5,200)]):
subs(0=NULL,op([1,1,3],R)); # Robert Israel, Mar 04 2016
  • PARI
    sqrt(-1+O(5^100))

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com) and Jason Earls, Jun 15 2001
Name corrected by Robert Israel at the suggestion of Wolfdieter Lang, Mar 04 2016
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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