Maxim Skorohodov - cp's OEIS frontend

A336604 a(0) = 1, a(1) = 2; thereafter let x = (a(n-1) mod a(n-2)); then a(n) = a(n-1) + a(x) if x < n, otherwise a(n) = a(n-1).

1, 2, 3, 5, 8, 13, 26, 27, 29, 32, 37, 50, 50, 51, 53, 56, 61, 74, 125, 125, 126, 128, 131, 136, 149, 200, 200, 201, 203, 206, 211, 224, 275, 275, 276, 278, 281, 286, 299, 350, 350, 351, 353, 356, 361, 374, 425, 425, 426, 428, 431, 436, 449, 500, 936, 936, 937, 939, 942, 947, 960, 1011

Offset: 0

Maxim Skorohodov, Oct 10 2020

nonn

			a(7) = 27, a(8) = 29, so a(9) = 29 + a(29 mod 27) = 32.

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Cf. A215526.

a:= proc(n) option remember; `if`(n<2, n+1, (x->
      a(n-1)+`if`(xAlois P. Heinz, Oct 25 2020

a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1] + If[(r = Mod[a[n - 1], a[n - 2]]) < n, a[r], 0]; Array[a, 51, 0] (* Amiram Eldar, Oct 10 2020 *)

A328820 Fourth digit after decimal point of square root of n.

Original entry on oeis.org

0, 2, 0, 0, 0, 4, 7, 4, 0, 2, 6, 1, 5, 6, 9, 0, 1, 6, 8, 1, 5, 4, 8, 9, 0, 0, 1, 5, 1, 2, 7, 8, 5, 9, 0, 0, 7, 4, 9, 5, 1, 7, 4, 2, 2, 3, 6, 2, 0, 0, 4, 1, 1, 4, 1, 3, 8, 7, 1, 9, 2, 0, 2, 0, 2, 0, 3, 2, 6, 6, 1, 2, 0, 3, 2, 7, 9, 7, 1, 2, 0, 3, 4, 1, 5, 6, 3, 8, 9, 8, 3, 6, 6, 3, 7, 9, 8, 4, 8, 0

Offset: 1

Maxim Skorohodov, Oct 28 2019

			sqrt(5) = 2.23606798..., so a(5) = 0.

Maxim Skorohodov, Table of n, a(n) for n = 1..10000

Cf. A111862, A023961.

a(n) = A010879(A000196(100000000*n)).

A328819 Third digit after decimal point of square root of n.

Original entry on oeis.org

0, 4, 2, 0, 6, 9, 5, 8, 0, 2, 6, 4, 5, 1, 2, 0, 3, 2, 8, 2, 2, 0, 5, 8, 0, 9, 6, 1, 5, 7, 7, 6, 4, 0, 6, 0, 2, 4, 4, 4, 3, 0, 7, 3, 8, 2, 5, 8, 0, 1, 1, 1, 0, 8, 6, 3, 9, 5, 1, 5, 0, 4, 7, 0, 2, 4, 5, 6, 6, 6, 6, 5, 4, 2, 0, 7, 4, 1, 8, 4, 0, 5, 0, 5, 9, 3, 7, 0, 3, 6, 9, 1, 3, 5, 6, 7, 8, 9, 9, 0

Offset: 1

Maxim Skorohodov, Oct 28 2019

			sqrt(21) = 4.58257569..., so a(21) = 2.

Maxim Skorohodov, Table of n, a(n) for n = 1..10000

Cf. A023961 (1st digit), A111862 (2nd digit).

Cf. A000196, A010879.

a(n) = floor(10^3*sqrt(n)) % 10; \\ Jinyuan Wang, Nov 03 2019

a(n) = A010879(A000196(1000000*n)).

A309872 For each term, take the last digit of the previous term and count all the appearances of that digit up to and including the previous term; the first term is 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 12, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 16, 3, 3, 4, 3, 5, 3, 6, 4, 4, 5, 4, 6, 5, 5, 6, 6, 7, 3, 7, 4, 7, 5, 7, 6, 8, 3, 8, 4, 8, 5, 8, 6, 9, 3, 9, 4, 9, 5, 9, 6, 10, 3, 10, 4, 10, 5, 10, 6, 11, 23, 11

Offset: 1

Maxim Skorohodov, Aug 21 2019

			To get the eleventh term, you need to get the last digit of the tenth term, which is 1, and then count all the 1's already in the sequence: 1, 1, 2, 1, 3, 1, 4, 1, 5, 1; there are six 1's, so the eleventh term is 6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A248034 (first term is 0).

Q:= Array(0..9):
A:= Vector(100):
Q[1]:= 1:
A[1]:= 1:
for n from 2 to 100 do
  d:= A[n-1] mod 10;
  A[n]:= Q[d];
  L:= convert(%,base,10);
  for i in L do Q[i]:= Q[i]+1 od
od:
convert(A,list); # Robert Israel, Feb 18 2020

f = vector(base=10); for (n=1, 91, v = if (n==1, 1, f[1+(v%base)]); apply (d -> f[1+d]++, if (v, digits(v, base), [0])); print1 (v ", ")) \\ Rémy Sigrist, Aug 21 2019

s, a, n = "1", [1], 1
while n < 100:
    n = n+1
    d = s[len(s)-1]
    i, aa = 0, 0
    while i < len(s):
        if s[i] == d:
            aa = aa+1
        i = i+1
    s, a = s+str(aa), a+[aa]
for n in range(1, 92): print(a[n-1], end=', ') # A.H.M. Smeets, Aug 22 2019

cp's OEIS Frontend

User: Maxim Skorohodov

A336604 a(0) = 1, a(1) = 2; thereafter let x = (a(n-1) mod a(n-2)); then a(n) = a(n-1) + a(x) if x < n, otherwise a(n) = a(n-1).

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A328820 Fourth digit after decimal point of square root of n.

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A328819 Third digit after decimal point of square root of n.

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Formula

A309872 For each term, take the last digit of the previous term and count all the appearances of that digit up to and including the previous term; the first term is 1.

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Author

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Examples

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Programs

Maple

PARI

Python