The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324153 Digits of one of the four 13-adic integers 3^(1/4) that is congruent to 11 mod 13. 12
 11, 10, 5, 11, 0, 6, 0, 8, 4, 6, 11, 2, 8, 6, 5, 4, 2, 11, 0, 3, 3, 5, 12, 0, 9, 6, 8, 7, 1, 0, 9, 1, 3, 7, 4, 8, 8, 10, 5, 8, 1, 4, 8, 2, 11, 12, 10, 11, 8, 9, 1, 5, 9, 6, 9, 10, 6, 5, 9, 6, 11, 12, 9, 12, 1, 4, 1, 6, 1, 12, 9, 7, 8, 5, 3, 2, 0, 6, 1, 7, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One of the two square roots of A322087, where an A-number represents a 13-adic number. The other square root is A324085. For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots. LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Wikipedia, p-adic number FORMULA Equals A324086*A286839 = A324087*A286838. a(n) = (A324084(n+1) - A324084(n))/13^n. For n > 0, a(n) = 12 - A324085(n). EXAMPLE The unique number k in [1, 13^3] and congruent to 11 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 986 = (5AB)_13, so the first three terms are 11, 10 and 5. MAPLE R:= select(t -> op([1, 3, 1], t)=11, [padic:-rootp(x^4-3, 13, 101)]): op([1, 1, 3], R); # Robert Israel, Sep 08 2019 PROG (PARI) a(n) = lift(-sqrtn(3+O(13^(n+1)), 4) * sqrt(-1+O(13^(n+1))))\13^n CROSSREFS Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324086, A324087. Sequence in context: A256078 A078200 A105034 * A065001 A022967 A023453 Adjacent sequences:  A324150 A324151 A324152 * A324154 A324155 A324156 KEYWORD nonn,base AUTHOR Jianing Song, Sep 01 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 08:44 EDT 2020. Contains 336369 sequences. (Running on oeis4.)