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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319664 Irregular triangle read by rows: T(n,k) = (-3)^k mod 2^n, n >= 2, 0 <= k <= 2^(n-2) - 1. 1
 1, 1, 5, 1, 13, 9, 5, 1, 29, 9, 5, 17, 13, 25, 21, 1, 61, 9, 37, 17, 13, 25, 53, 33, 29, 41, 5, 49, 45, 57, 21, 1, 125, 9, 101, 81, 13, 89, 117, 33, 29, 41, 5, 113, 45, 121, 21, 65, 61, 73, 37, 17, 77, 25, 53, 97, 93, 105, 69, 49, 109, 57, 85 (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, 13, 9, 5, 1, 29, 9, 5, 17, 13, 25, 21, 1, 61, 9, 37, 17, 13, 25, 53, 33, 29, 41, 5, 49, 45, 57, 21, 1, 125, 9, 101, 81, 13, 89, 117, 33, 29, 41, 5, 113, 45, 121, 21, 65, 61, 73, 37, 17, 77, 25, 53, 97, 93, 105, 69, 49, 109, 57, 85 ... PROG (PARI) T(n, k) = lift(Mod(-3, 2^n)^k) CROSSREFS Cf. A007814, A319666. Sequence in context: A104793 A243883 A147004 * A205961 A146620 A300291 Adjacent sequences: A319661 A319662 A319663 * A319665 A319666 A319667 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 February 4 19:02 EST 2023. Contains 360059 sequences. (Running on oeis4.)