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

0,2

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

Formula

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

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 *)

Prog

(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 */

Crossrefs

Cf. A034939, A048898, A048899.

Sequence in context: A175818 A034939 A048898 * A337833 A294948 A178769

Adjacent sequences: A034932 A034933 A034934 * A034936 A034937 A034938

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved