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 1-10 of 10 results.

A064801 Take 1, skip 2, take 2, skip 3, take 3, etc.

Original entry on oeis.org

1, 4, 5, 9, 10, 11, 16, 17, 18, 19, 25, 26, 27, 28, 29, 36, 37, 38, 39, 40, 41, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 69, 70, 71, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 121, 122, 123, 124, 125, 126, 127, 128
Offset: 1

Views

Author

Robert G. Wilson v, Oct 21 2001

Keywords

Comments

A253607(a(n)) < 0. - Reinhard Zumkeller, Jan 05 2015
Integers m such that A000196(m) = A079643(m). - Firas Melaih, Dec 10 2020
Also possible values of floor(x*floor(x)) for real x >= 1. - Jianing Song, Feb 16 2021

Links

Crossrefs

Cf. A007606, A004202, A048859.
Cf. A061885 (complement), A253607.
Cf. A136272.

Programs

  • Haskell
    a064801 n = a064801_list !! (n-1)
a064801_list = f 1 [1..] where
   f k xs = us ++ f (k + 1) (drop (k + 1) vs)
            where (us, vs) = splitAt k xs
-- Reinhard Zumkeller, May 16 2014
  • Maple
    seq(`if`(floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k, k, NULL), k = 0..2034); # a(1)..a(1000), Rainer Rosenthal, Jul 19 2024
  • Mathematica
    a = Table[n, {n, 0, 200} ]; b = {}; Do[a = Drop[a, {1, n} ]; b = Append[b, Take[a, {1, n} ]]; a = Drop[a, {1, n} ], {n, 1, 14} ]; Flatten[b]
Flatten[Table[Range[n^2,n^2+n-1],{n,12}]] (* Harvey P. Dale, Dec 18 2015 *)
  • PARI
    { n=0; for (m=1, 10^9, s=m^2; a=0; for (k=0, m - 1, a=s+k; write("b064801.txt", n++, " ", a); if (n==1000, return)) ) } \\ Harry J. Smith, Sep 26 2009
  • Python
    from math import isqrt  # after Rainer Rosenthal
def isA(k: int): return k < ((s:=isqrt(k)) * (s + 1))
print([k for k in range(129) if isA(k)]) # Peter Luschny, Jul 19 2024

Formula

a(n) = A004202(n) - 1.
Can be interpreted as a table read by rows: T(n,k) = n^2 + k, 0 <= k < n. T(n,k) = 0 iff k > A000196(n); T(n,0) = A000290(n); T(n,1) = A002522(n) for n > 1; T(n,2) = A010000(n) = A059100(n) for n > 2; T(n, n-3) = A014209(n-1) for n > 2; T(n, n-2) = A028552(n) for n > 1; T(n, n-1) = A028387(n-1); T(2*n+1, n) = A001107(n+1). - Reinhard Zumkeller, Nov 18 2003
Numbers k such that floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k. - Rainer Rosenthal, Jul 19 2024

A137894 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value n.

Original entry on oeis.org

1, 3, 3, 4, 7, 9, 7, 12, 9, 10, 11, 17, 13, 21, 21, 16, 17, 27, 19, 38, 21, 33, 23, 24, 25, 39, 27, 28, 41, 30, 31, 48, 33, 51, 49, 51, 37, 57, 39, 40, 41, 63, 43, 44, 63, 69, 47, 72, 49, 75, 51, 52, 53, 81, 77, 84, 57, 78, 59, 90, 61, 93, 63, 64, 91, 99, 67, 68, 69, 99
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

Links

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272.

Programs

  • Maple
    mx:= 10000: # maximal index needed
b:= proc(n) n end:
a:= proc(n) option remember; global mx; local h, t;
      if n=0 then 0 else a(n-1); t:= b(n);
        if n+t<=mx then h:=b(t+n); b(t+n):=h+n fi; t
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 04 2015
  • Mathematica
    mx = 10000 (* maximal index needed *); b[n_] := n; a[n_] := a[n] = Module[{h, t}, If[n == 0, 0, a[n-1]; t = b[n]; If[n+t <= mx, h = b[t+n]; b[t+n] = h+n]; t]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 24 2016, after Alois P. Heinz *)
  • Python
    TOP = 1000
a = [1]*TOP
for n in range(1,TOP):
  a[n]=n
for n in range(1,TOP):
  print(str(a[n]),end=',')
  if n+a[n]Alex Ratushnyak, Nov 22 2013

Formula

Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value n.

Extensions

More terms from Alex Ratushnyak, Nov 22 2013.

A137832 Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the last digit in the term at position n + a(n).

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 10, 11, 1, 1, 1, 16, 1, 1, 1, 21, 2, 23, 2, 25, 2, 27, 2, 29, 3, 31, 3, 3, 34, 3, 3, 37, 3, 3, 40, 4, 43, 44, 45, 47, 48, 49, 5, 51, 52, 53, 5, 5, 56, 57, 5, 5, 6, 61, 6, 6, 6, 65, 6, 67, 69, 7, 7, 72, 7, 7, 75, 76, 7, 7, 79, 8, 82, 83, 84, 8
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 29 2008

Keywords

Examples

			First few steps are:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 1; delete the last digit in the term at position 1+a(1) = 2: 2;
1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 2; delete the last digit in the term at position 2+a(2) = 5: 6;
1,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 3; delete the last digit in the term at position 3+a(3) = 7: 9;
1,3,4,5,7,8,10,11,12,13,14,15,16,17,18,19,20,...
n = 4; delete the last digit in the term at position 4+a(4) = 9: 2;
1,3,4,5,7,8,10,11,1,13,14,15,16,17,18,19,20,...
n = 5; delete the last digit in the term at position 5+a(5) = 12: 5;
1,3,4,5,7,8,10,11,1,13,14,1,16,17,18,19,20,...
n = 6; delete the last digit in the term at position 6+a(6) = 14: 8;
1,3,4,5,7,8,10,11,1,13,14,1,16,17,1,19,20,...

Links

Crossrefs

Cf. A137292, A136120, A136119, A136259, A136272, A137319, A137417, A137418.

A137901 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value 1.

Original entry on oeis.org

1, 3, 3, 4, 6, 7, 7, 9, 9, 10, 12, 12, 14, 15, 15, 16, 18, 19, 19, 21, 21, 22, 24, 25, 25, 26, 28, 28, 30, 31, 31, 33, 33, 34, 36, 36, 38, 39, 39, 40, 42, 43, 43, 45, 45, 46, 48, 48, 50, 51, 51, 53, 53, 54, 56, 57, 57, 58, 60, 60, 62, 63, 63, 64, 66, 67, 67, 69, 69, 70
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272.

Programs

  • PARI
    lista(nn) = my(va = [1..nn]); for (n=1, nn, my(m = n+va[n]); if (m <= nn, va[m]++)); va; \\ Michel Marcus, Oct 29 2022

Formula

Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value 1.

Extensions

Entries corrected and extended by Paolo P. Lava, Mar 10 2009
More terms from Michel Marcus, Oct 29 2022

A137902 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value 1 if the term is odd, otherwise divide the term by 2.

Original entry on oeis.org

1, 1, 4, 4, 5, 6, 8, 4, 9, 5, 11, 3, 13, 14, 4, 16, 17, 9, 20, 20, 21, 11, 23, 24, 25, 13, 28, 14, 29, 30, 31, 16, 34, 17, 35, 36, 37, 38, 20, 20, 41, 22, 43, 44, 45, 23, 47, 12, 49, 25, 52, 52, 53, 54, 56, 56, 57, 29, 60, 16, 61, 31, 63, 32, 65, 66, 68, 68, 70, 35
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272.

Programs

  • PARI
    lista(nn) = my(va = [1..nn]); for (n=1, nn, my(m = n+va[n]); if (m <= nn, if (va[m] % 2, va[m]++, va[m] /= 2));); va; \\ Michel Marcus, Oct 29 2022

Extensions

More terms from Michel Marcus, Oct 29 2022

A166021 a(n) = 2*A000124(A003056(n-1)) if A002262(n-1)=0, otherwise a(n-1)+1.

Original entry on oeis.org

2, 4, 5, 8, 9, 10, 14, 15, 16, 17, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 44, 45, 46, 47, 48, 49, 50, 58, 59, 60, 61, 62, 63, 64, 65, 74, 75, 76, 77, 78, 79, 80, 81, 82, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121
Offset: 1

Views

Author

Antti Karttunen, Oct 05 2009

Keywords

Crossrefs

Complement of A136272.

A137838 Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the first digit in the term at position n + a(n).

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 10, 11, 2, 13, 4, 5, 16, 7, 8, 19, 21, 2, 23, 4, 5, 6, 7, 8, 29, 0
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 29 2008

Keywords

Examples

			First few steps are:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 1; delete the first digit in the term at position 1+a(1) = 2: 2;
1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 2; delete the first digit in the term at position 2+a(2) = 5: 6;
1,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 3; delete the first digit in the term at position 3+a(3) = 7: 9;
1,3,4,5,7,8,10,11,12,13,14,15,16,17,18,19,20,...
n = 4; delete the first digit in the term at position 4+a(4) = 9: 1;
1,3,4,5,7,8,10,11,2,13,14,15,16,17,18,19,20,...
n = 5; delete the first digit in the term at position 5+a(5) = 12: 1;
1,3,4,5,7,8,10,11,2,13,14,5,16,17,18,19,20,...
n = 6; delete the first digit in the term at position 6+a(6) = 14: 1;
1,3,4,5,7,8,10,11,2,13,14,5,16,7,18,19,20,...

Crossrefs

Cf. A137292, A136120, A136119, A136259, A136272, A137319, A137417, A137418.

A137898 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value of the term at position n+a(n)+1.

Original entry on oeis.org

1, 5, 3, 4, 5, 21, 15, 17, 9, 21, 11, 12, 13, 14, 15, 16, 17, 37, 19, 20, 21, 68, 23, 75, 51, 81, 55, 57, 29, 93, 63, 65, 33, 69, 35, 36, 37, 77, 39, 81, 41, 85, 43, 44, 45, 93, 47, 48
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272.

Formula

Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value of the term at position n+a(n)+1.

Extensions

Entries corrected and extended by Paolo P. Lava, Mar 10 2009

A137903 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value a(n) if the term is odd, else divide the term by 2.

Original entry on oeis.org

1, 1, 4, 4, 5, 6, 11, 4, 9, 5, 11, 3, 13, 14, 10, 16, 17, 18, 19, 20, 21, 11, 23, 24, 35, 13, 27, 14, 29, 30, 31, 16, 44, 17, 35, 18, 37, 19, 52, 20, 41, 35, 43, 44, 45, 23, 47, 12, 49, 50, 68, 52, 53, 45, 55, 56, 76, 29, 59, 47, 61, 31, 63, 64, 65, 66, 67, 68, 92, 35
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272, A137901, A137902.

Programs

  • PARI
    lista(nn) = my(va = [1..nn]); for (n=1, nn, my(m = n+va[n]); if (m <= nn, if (va[m] % 2, va[m]+=va[n], va[m] /= 2));); va; \\ Michel Marcus, Oct 29 2022

Extensions

Entries corrected and extended by Paolo P. Lava, Mar 10 2009
More terms from Michel Marcus, Oct 29 2022

A138095 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add: to the term at position n + 1*a(n) the value 1, to the term at position n + 2*a(n) the value 1, ..., to the term at position n + n*a(n) the value 1.

Original entry on oeis.org

1, 3, 3, 4, 6, 7, 7, 10, 10, 10, 12, 14, 14, 15, 15, 17, 18, 19, 20, 23, 22, 22, 25, 24, 25, 27, 29, 30, 32, 32, 31, 32, 34, 35, 39, 36, 38, 39, 41, 42, 43, 43, 45, 46, 46, 46, 48, 52, 51, 53, 51, 52, 55, 55, 56, 59, 57, 60, 63, 62, 62, 64, 63, 65, 66, 68, 69, 70, 72, 71
Offset: 1

Views

Author

Ctibor O. Zizka, May 03 2008

Keywords

Examples

			        n | 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
  --------+-----------------------------------------------------------
  Step  1 |    3
  Step  2 |             6        9
  Step  3 |                7       10       13
  Step  4 |                     10          14          17          21
  Step  5 |                              12                18
  Step  6 |                                    14                   22
  Step  7 |                                       15
  Step  8 |                                                   19
  Step  9 |                                                      20
  Step 10 |                                                         23
  --------+-----------------------------------------------------------
     a(n) | 1  3  3  4  6  7  7 10 10 10 12 14 14 15 15 17 18 19 20 23

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272, A137292, A136120, A137832, A137838, A137894, A137898, A137901, A137902, A137903.

Programs

  • PARI
    lista(nn) = my(va = [1..nn]); for (n=1, nn, for (k=1, n, my(j = n+k*va[n]); if (j <= #va, va[j]++); )); va; \\ Michel Marcus, Aug 09 2022

Extensions

Corrected and extended by Michel Marcus, Aug 09 2022
Showing 1-10 of 10 results.

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