cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A064536 a(n) = (4^n mod 3^n) mod 2^n.

Original entry on oeis.org

1, 3, 2, 13, 20, 3, 51, 87, 121, 711, 1139, 3537, 8034, 15752, 27922, 49629, 33201, 35975, 143900, 136341, 545364, 2181456, 1060135, 4240540, 16962160, 28647197, 13597858, 205877827, 100616667, 381266393, 1397863922, 3825576990, 8216376565, 14181633879, 22366797148
Offset: 1

Views

Author

Labos Elemer, Oct 08 2001

Keywords

Comments

A generalization of A002380. It arises also as a coefficient (=c1) of 1^n=1 in a special (greedy) decomposition of 4^n into like powers as follows: 4^n = c3*3^n + c2*2^n + c1*1^n.

Links

Crossrefs

Cf. A002380, A064853-A064855, A060692, A064628-A064631.

Programs

  • Mathematica
    Table[Mod[PowerMod[4,n,3^n],2^n],{n,40}] (* Harvey P. Dale, Apr 09 2013 *)
  • PARI
    a(n) = { (4^n % 3^n) % 2^n } \\ Harry J. Smith, Sep 17 2009

Formula

n = 7: 4^7 = 16384 = 7*2187 + 8*128 + 51*1 where a(7)=51, the last coefficient; A064630(7) = 7 + 8 + a(7) = 66.

A064855 a(n) = (((6^n mod 5^n) mod 4^n) mod 3^n) mod 2^n.

Original entry on oeis.org

1, 2, 0, 14, 16, 10, 66, 21, 321, 917, 2037, 1550, 2420, 15152, 27439, 46731, 110953, 137148, 336949, 703202, 805647, 181132, 5835407, 3343039, 21816283, 18528238, 95129681, 241918238, 311938330, 48698222, 1539688558, 3481498150, 8104918325, 13512884439, 22365723609
Offset: 1

Views

Author

Labos Elemer, Oct 08 2001

Keywords

Comments

A generalization of A002380, A064536 and A064854. It arises also as a coefficient (=c1) of 1^n=1 in a special (greedy) decomposition of 6^n into like powers as follows: 6^n = c5*5^n + c4*4^n + c3*3^n + c2*2^n + c1*1^n.

Links

Crossrefs

Cf. A002380, A064536, A064854, A064855, A060692, A064628-A064631.

Programs

  • Mathematica
    Table[Fold[Mod,6^n,Range[5,2,-1]^n],{n,40}]  (* Harvey P. Dale, Mar 14 2011 *)
  • PARI
    a(n) = { (((6^n%5^n)%4^n)%3^n)%2^n } \\ Harry J. Smith, Sep 28 2009

Formula

n = 8: 6^8 = 1679616 = 4*390625 + 1*65536 + 7*6561 + 22*256 + 21*1 where a(8)=21, the last coefficient and here 6^8 is decomposed into 4 + 1 + 7 + 22 + 21 = 55 like (8th) powers.

A064854 a(n) = ((5^n mod 4^n) mod 3^n) mod 2^n.

Original entry on oeis.org

1, 0, 7, 0, 21, 37, 118, 56, 19, 428, 808, 3920, 2256, 15240, 28312, 46733, 128931, 251439, 434788, 645833, 1397733, 1179155, 7185704, 1551886, 33308648, 65879944, 121274199, 65829274, 228529703, 248939750, 799831532, 2835988891, 1358930753, 9419331043, 9093076436
Offset: 1

Views

Author

Labos Elemer, Oct 08 2001

Keywords

Comments

A generalization of A002380 and A064536. It arises also as a coefficient (=c1) of 1^n=1 in a special (greedy) decomposition of 5^n into like powers as follows: 5^n = c4*4^n + c3*3^n + c2*2^n + c1*1^n.

Links

Crossrefs

Cf. A002380, A064536, A064855, A060692, A064628-A064631.

Programs

Formula

n = 7: 5^7 = 78125 = 4*16384 + 5*2187 + 12*128 + 118*1, where a(7)=118, the last coefficient.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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