A136120 -id:A136120 - cp's OEIS frontend

A139419 a(n) = first term of the n-th run of consecutive numbers in A136120.

1, 3, 9, 15, 22, 36, 48, 69, 87, 116, 141, 167, 194, 222, 269, 308, 368, 419, 471, 524, 578, 633, 719, 791, 896, 986, 1077, 1169, 1262, 1356, 1451, 1591, 1710, 1876, 2020, 2213, 2383, 2604, 2801, 3051, 3276, 3502, 3729, 3957, 4186, 4416, 4647, 4879, 5112

Offset: 1

Klaus Brockhaus, Apr 22 2008

nonn

			A136120 starts 1, 3, 4, 5, 9, 10, 15, ..., so a(1) = 1, a(2) = 3, a(3) = 9.

Klaus Brockhaus, Table of n, a(n) for n=1..396

Cf. A136120, A139418, A139420.

f[seq_] := Module[{s = seq, n1, n2}, n++; n1 = s[[n]] + n; If[n1 <= len, n2 = Min[n - 1 + 2*s[[n]], len]; len -= n2 - n1 + 1; Drop[s, {n1, n2}], s]]; n = 0; len = 5200; First /@Split[FixedPoint[f, Range[len]], #2 - #1 == 1 &] (* Jayanta Basu, Jun 15 2013 - using the Mma program in A136120 *)

A139420 a(n) = length of n-th run of consecutive numbers in A136120.

Original entry on oeis.org

1, 3, 2, 2, 5, 2, 6, 2, 7, 2, 2, 2, 2, 11, 2, 12, 2, 2, 2, 2, 2, 17, 2, 18, 2, 2, 2, 2, 2, 2, 24, 2, 25, 2, 26, 2, 27, 2, 28, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 38, 2, 39, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 50, 2, 51, 2, 52, 2, 53, 2, 54, 2, 55, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 71, 2, 72, 2, 2, 2

Offset: 1

Klaus Brockhaus, Apr 22 2008

nonn

			A136120 starts 1, 3, 4, 5, 9, 10, 15, ..., so a(1) = 1, a(2) = 3, a(3) = 2.

Klaus Brockhaus, Table of n, a(n) for n=1..395

Cf. A136120, A139418, A139419.

f[seq_] := Module[{s = seq, n1, n2}, n++; n1 = s[[n]] + n; If[n1 <= len, n2 = Min[n - 1 + 2*s[[n]], len]; len -= n2 - n1 + 1; Drop[s, {n1, n2}], s]]; n = 0; len = 29800; Length /@Split[FixedPoint[f, Range[len]], #2 - #1 == 1 &]  (* Jayanta Basu, Jun 15 2013 - using the Mma program in A136120 *)

A139418 Complement of A136120.

Original entry on oeis.org

2, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 94, 95, 96, 97, 98, 99, 100, 101

Offset: 1

Klaus Brockhaus, Apr 22 2008

k-th run of consecutive numbers has length A136120(k).

			A136120 starts 1, 3, 4, 5, 9, 10, 15, ..., so sequence starts 2, 6, 7, 8, 11, 12, ... .

Cf. A136120, A139419, A139420.

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

Ctibor O. Zizka, Apr 29 2008

			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,...

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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

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

Ctibor O. Zizka, Apr 29 2008

			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,...

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

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

Ctibor O. Zizka, May 03 2008

			        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

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

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

Corrected and extended by Michel Marcus, Aug 09 2022

cp's OEIS Frontend

A139419 a(n) = first term of the n-th run of consecutive numbers in A136120.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A139420 a(n) = length of n-th run of consecutive numbers in A136120.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A139418 Complement of A136120.

Views

Author

Keywords

Comments

Examples

Crossrefs

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).

Views

Author

Keywords

Examples

Links

Crossrefs

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).

Views

Author

Keywords

Examples

Crossrefs

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Extensions

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