Tristan Young - cp's OEIS frontend

User: Tristan Young

Tristan Young has authored 2 sequences.

A346035 a(1) = 1; if a(n) is not divisible by 3, a(n+1) = 4*a(n) + 1, otherwise a(n+1) = a(n)/3.

1, 5, 21, 7, 29, 117, 39, 13, 53, 213, 71, 285, 95, 381, 127, 509, 2037, 679, 2717, 10869, 3623, 14493, 4831, 19325, 77301, 25767, 8589, 2863, 11453, 45813, 15271, 61085, 244341, 81447, 27149, 108597, 36199, 144797, 579189, 193063, 772253, 3089013, 1029671, 4118685

Offset: 1

Tristan Young, Jul 02 2021

Tristan Young, Table of n, a(n) for n = 1..15000
Tristan Young, C code to generate a b-file for the first 15000 terms of this sequence

Cf. A006370, A128333, A153727.

a[1] = 1; a[n_] := a[n] = If[Divisible[a[n-1],3], a[n-1]/3, 4*a[n-1]+1]; Array[a, 50] (* Amiram Eldar, Jul 12 2021 *)

a(n) = if (n==1, 1, my(x=a(n-1)); if (x % 3, 4*x+1, x/3)); \\ Michel Marcus, Aug 12 2021

// generates all the numbers in the sequence before it first surpasses 1 billion
int n;
void setup() {
  n = 1;
  noLoop();
}
void draw() {
  print(n + ",");
  while (true) {
    if (n % 3 == 0) {
      n /= 3;
    } else {
      n *= 4; n++;
    }
    print(n);
    if (n == 1 || n >= 600000000) {
      break;
    } else {
      print(", ");
    }
  }
}

A330489 a(n) is equal to a(n-1) plus (a(n-1) written in base n but interpreted in base n+1), with a(1)=1.

Original entry on oeis.org

1, 2, 4, 9, 19, 41, 87, 193, 427, 940, 2049, 4619, 10363, 22921, 50522, 111018, 248438, 554112, 1232067, 2723158, 6003186, 13446356, 30050952, 66594552, 147234100, 324832999, 714046741, 1585188074, 3511557725, 7762753394, 17129248715, 37693951852, 82773271861

Offset: 1

Tristan Young, Dec 15 2019

			Given the 5th term in the sequence, the next (6th) term is the 5th term plus the result obtained by taking the 5th term's digits in order in base 6 (the index of the next term) and incrementing the base by 1 without changing the digits.
In this example, a(5) = 19 = 31_6; incrementing the base of 31_6 without changing the digits gives 31_7 = 22, and a(6) = a(5) + 22 = 19 + 22 = 41.
.
                      digits
                      of a(n-1)
             a(n-1)   interpreted
             in       in base n+1
  n  a(n-1)  base n   = k             k + a(n-1) = a(n)
  -  ------  ------   -----------   -------------------
  1                                                   1
  2     1      1_2      1_3 =   1     1 +   1    =    2
  3     2      2_3      2_4 =   2     2 +   2    =    4
  4     4     10_4     10_5 =   5     5 +   4    =    9
  5     9     14_5     14_6 =  10    10 +   9    =   19
  6    19     31_6     31_7 =  22    22 +  19    =   41
  7    41     56_7     56_8 =  46    46 +  41    =   87
  8    87    127_8    127_9 = 106   106 +  87    =  193

a[n_] := a[n] = a[n-1] + FromDigits[ IntegerDigits[ a[n-1], n], n + 1]; Array[a, 33] (* Giovanni Resta, Dec 16 2019 *)

lista(nn) = {my(a = 1); print1(a, ", "); for (n=2, nn, a += fromdigits(digits(fromdigits(digits(a, n), n+1))); print1(a, ", "););} \\ Michel Marcus, Dec 16 2019

cp's OEIS Frontend

User: Tristan Young

A346035 a(1) = 1; if a(n) is not divisible by 3, a(n+1) = 4*a(n) + 1, otherwise a(n+1) = a(n)/3.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Processing