A034935 Successive approximations to 5-adic integer sqrt(-1).

0, 2, 7, 57, 182, 2057, 14557, 45807, 280182, 6139557, 25670807, 123327057, 5006139557, 11109655182, 102662389557, 407838170807, 3459595983307, 79753541295807, 365855836217682, 2273204469030182, 49956920289342682

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

This is the root congruent to 2 mod 5.

References

• J. H. Conway, The Sensual Quadratic Form, p. 118.
• K. Mahler, Introduction to p-Adic Numbers and Their Functions, Cambridge, 1973, p. 35.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1121

Crossrefs

Cf. A034939, A048898, A048899.

Programs

Mathematica

Table[ PowerMod[2, 5^n, 5^n], {n, 0, 24}] // Union (* Jean-François Alcover, Dec 03 2012, from formula given by Joe K. Crump *)

PARI

sqrt(-1+O(5^40))

PARI

{a(n) = local(k, x, y); for(i = 0, n, until( x != (y = truncate( sqrt( -1 + O(5^(k++))))), x = y));x} /* Michael Somos, Mar 03 2008 */

Formula

Successive values of 2^(5^x) mod 5^x. - Joe K. Crump (joecr(AT)carolina.rr.com), Jan 20 2001