The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319663 Irregular triangle read by rows: T(n,k) = 5^k mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1. 1
 1, 1, 5, 1, 5, 9, 13, 1, 5, 25, 29, 17, 21, 9, 13, 1, 5, 25, 61, 49, 53, 9, 45, 33, 37, 57, 29, 17, 21, 41, 13, 1, 5, 25, 125, 113, 53, 9, 45, 97, 101, 121, 93, 81, 21, 105, 13, 65, 69, 89, 61, 49, 117, 73, 109, 33, 37, 57, 29, 17, 85, 41, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS The n-th row contains 2^(n-2) numbers, and is a permutation of 1, 5, 9, ..., 2^n - 3. For e >= 4, the multiplicative order of a modulo 2^e equals to 2^(e-2) iff a == 3, 5 (mod 8); for e >= 5, the multiplicative order of a modulo 2^e equals to 2^(e-3) iff a == 7, 9 (mod 16); for e >= 6, the multiplicative order of a modulo 2^e equals to 2^(e-4) iff a == 15, 17 (mod 32), etc. From this we can see v(T(n,k) - 1, 2) = v(k, 2) + 2, where v(k, 2) = A007814(k) is the 2-adic valuation of k. Also, T(n,k) is a 2^v(k, 2)-th power residue but not a 2^(v(k, 2)+1)-th power residue modulo 2^i, i >= v(k, 2) + 3. LINKS EXAMPLE Table begins 1, 1, 5, 1, 5, 9, 13, 1, 5, 25, 29, 17, 21, 9, 13, 1, 5, 25, 61, 49, 53, 9, 45, 33, 37, 57, 29, 17, 21, 41, 13, 1, 5, 25, 125, 113, 53, 9, 45, 97, 101, 121, 93, 81, 21, 105, 13, 65, 69, 89, 61, 49, 117, 73, 109, 33, 37, 57, 29, 17, 85, 41, 77 ... PROG (PARI) T(n, k) = lift(Mod(5, 2^n)^k) CROSSREFS Cf. A007814, A319665. Sequence in context: A128359 A340213 A170903 * A255166 A131113 A139426 Adjacent sequences: A319660 A319661 A319662 * A319664 A319665 A319666 KEYWORD nonn,tabf AUTHOR Jianing Song, Sep 25 2018 STATUS approved

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

Last modified March 25 23:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)