This site is supported by donations to The OEIS Foundation.
User:Enrique Pérez Herrero/Salad
From OeisWiki
Contents
FORMULAE SALAD
This is compilations of sequences that I egoistically need for other purposes, and it is very handy to have them already written somewhere:
NUMBER OF DIGITS
b | Sequence | Description |
---|---|---|
2 | A029837 | Binary order of n: log_2(n) rounded up to next integer. |
2 | A070939 | Length of binary representation of n. |
3 | A081604 | String-length of ternary representation of n. |
4 | A110591 | String length of base 4 representation of n. |
10 | A055642 | Number of digits in decimal expansion of n. |
The expression can be extended to any real number :
Mathematica Programming
(* NUMBER OF DIGITS related OEIS sequences *) Digits[x_,b_Integer:10]/;If[TrueQ[b > 1], True, Message[Digits::ibase, b]; False]:=Max[1+Floor[Log[b,Abs[x]]],1]; Digits::ibase="Base `1` is not an integer greater than 1"; A029837[n_]:=Ceiling[Log[2,n]]; A070939[n_]:=Digits[n,2]; A081604[n_]:=Digits[n,3]; A110591[n_]:=Digits[n,4]; A055642[n_]:=Digits[n]; (*Adding help*) Digits::usage="Digits[x] gives the number of digits in the base 10 representation of the integer part of the real number x. Digits[x,b] gives the number of digits in the base b representation of the integer part of x."; A029837::usage="A029837: Binary order of n: log_2(n) rounded up to next integer."; A055642::usage="A055642: Number of digits in decimal expansion of n."; A070939::usage="A070939: Length of binary representation of n."; A081604::usage="A081604: String-length of ternary representation of n."; A110591::usage="A110591: String length of base 4 representation of n. String length of A007090.";
k*n digit-reversed mod k
k | Sequence | Description |
---|---|---|
2 | A084052 | 2*n digit-reversed mod 2 |
3 | A000004 | 3*n digit-reversed mod 3 |
4 | A084053 | 4*n digit-reversed mod 4 |
5 | A084054 | 5*n digit-reversed mod 5 |
6 | A084055 | 6*n digit-reversed mod 6 |
7 | A084339 | 7*n digit-reversed mod 7 |
8 | A084340 | 8*n digit-reversed mod 8 |
9 | A000004 | 9*n digit-reversed mod 9 |
10 | A000030 | 10*n digit-reversed mod 10 |
13 | A084341 | 13*n digit-reversed mod 13 |
Formulae for k*n digit-reversed mod k
Initial digit of n: A000030
Mathematica Programming:
(*Adding help*) A000030::usage="A000030: Initial digit of n."; A055642::usage="A055642: Number of digits in decimal expansion of n.";