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 1-8 of 8 results.

A284069 Numbers whose smallest decimal digit is 8.

Original entry on oeis.org

8, 88, 89, 98, 888, 889, 898, 899, 988, 989, 998, 8888, 8889, 8898, 8899, 8988, 8989, 8998, 8999, 9888, 9889, 9898, 9899, 9988, 9989, 9998, 88888, 88889, 88898, 88899, 88988, 88989, 88998, 88999, 89888, 89889, 89898, 89899, 89988, 89989, 89998, 89999, 98888
Offset: 1

Views

Author

Jaroslav Krizek, Mar 24 2017

Keywords

Comments

Numbers n such that A054054(n) = 8.
Prime terms are in A020472. - Corrected by Robert Israel, Apr 05 2017

Links

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), this sequence (k = 8), A002283 (k = 9).
Cf. A020472, A054054.

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 8]
  • Maple
    F:= proc(d) local r; # to get all terms with d digits
r:= 8*(10^d-1)/9;
op(sort(convert(map(t -> r + add(10^(j-1),j=t), combinat:-powerset(d) minus {{$1..d}}),list)))
end proc:
map(F, [$1..5]); # Robert Israel, Apr 05 2017
  • Mathematica
    Flatten@ Table[ Most[ FromDigits /@ Tuples[{8,9}, k]], {k,5}] (* Giovanni Resta, Mar 24 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 8; \\ Michel Marcus, Mar 25 2017
  • Python
    print([n for n in range(8, 10**6) if min(str(n))=='8']) # Indranil Ghosh, Apr 06 2017

Formula

From Robert Israel, Apr 05 2017: (Start)
a(2*j+2^(m+1)-m-3) = 10*a(j+2^m-m-1)+8 for j=1..2^m-1.
a(2*j+2^(m+1)-m-2) = 10*a(j+2^m-m-1)+9 for j=1..2^m-1.
a(2^(m+1)-m-2) = 10^m-2. (End)

A284064 Numbers whose smallest decimal digit is 3.

Original entry on oeis.org

3, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93, 333, 334, 335, 336, 337, 338, 339, 343, 344, 345, 346, 347, 348, 349, 353, 354, 355, 356, 357, 358, 359, 363, 364, 365, 366, 367, 368, 369, 373, 374, 375, 376, 377, 378, 379, 383, 384, 385, 386, 387, 388
Offset: 1

Views

Author

Jaroslav Krizek, Mar 19 2017

Keywords

Comments

Numbers n such that A054054(n) = 3.
Prime terms are in A106103.

Links

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), this sequence (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 3]
  • Maple
    L[1]:= {3}: G[1]:= {$4..9}:
for n from 2 to 3 do L[n]:= map(t -> seq(10*t+j,j=3..9), L[n-1]) union map(t -> 10*t+3, G[n-1]);
  G[n]:= map(t -> seq(10*t+j,j=4..9), G[n-1])
od:
seq(op(sort(convert(L[n],list))),n=1..3); # Robert Israel, Mar 27 2017
  • Mathematica
    With[{k = 3}, Select[Range@ 388, And[Total@ Take[#, k] == 0, #[[k + 1]] > 0] &@ RotateRight@ DigitCount@ # &]] (* Michael De Vlieger, Mar 20 2017 *) (* or *)
Select[Range[10000], Min[IntegerDigits[#]] == 3 &] (* faster, simpler, Giovanni Resta, Mar 22 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 3; \\ Michel Marcus, Mar 25 2017

A284063 Numbers whose smallest decimal digit is 2.

Original entry on oeis.org

2, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92, 222, 223, 224, 225, 226, 227, 228, 229, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 245, 246, 247, 248, 249, 252, 253, 254, 255, 256, 257, 258, 259, 262, 263, 264, 265, 266, 267, 268
Offset: 1

Views

Author

Jaroslav Krizek, Mar 19 2017

Keywords

Comments

Numbers n such that A054054(n) = 2.
Prime terms are in A106102.

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), this sequence (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 2]
  • Mathematica
    Select[Range[300], Min[IntegerDigits[#]] == 2 &] (* Alonso del Arte, Mar 19 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 2; \\ Michel Marcus, Mar 25 2017
  • Python
    def ok(n): return '2' == min(str(n))
print([m for m in range(269) if ok(m)]) # Michael S. Branicky, Feb 22 2021

A284065 Numbers whose smallest decimal digit is 4.

Original entry on oeis.org

4, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94, 444, 445, 446, 447, 448, 449, 454, 455, 456, 457, 458, 459, 464, 465, 466, 467, 468, 469, 474, 475, 476, 477, 478, 479, 484, 485, 486, 487, 488, 489, 494, 495, 496, 497, 498, 499, 544, 545, 546, 547, 548, 549, 554
Offset: 1

Views

Author

Jaroslav Krizek, Mar 19 2017

Keywords

Comments

Numbers n such that A054054(n) = 4.
Prime terms are in A106104.

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), this sequence (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 4]
  • Mathematica
    With[{k = 4}, Select[Range@ 554, And[Total@ Take[#, k] == 0, #[[k + 1]] > 0] &@ RotateRight@ DigitCount@ # &]] (* Michael De Vlieger, Mar 20 2017 *)
(* or *)
Select[Range[1000], Min[IntegerDigits[#]] == 4 &] (* Giovanni Resta, Mar 22 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 4; \\ Michel Marcus, Mar 25 2017

A284066 Numbers whose smallest decimal digit is 5.

Original entry on oeis.org

5, 55, 56, 57, 58, 59, 65, 75, 85, 95, 555, 556, 557, 558, 559, 565, 566, 567, 568, 569, 575, 576, 577, 578, 579, 585, 586, 587, 588, 589, 595, 596, 597, 598, 599, 655, 656, 657, 658, 659, 665, 675, 685, 695, 755, 756, 757, 758, 759, 765, 775, 785, 795, 855
Offset: 1

Views

Author

Jaroslav Krizek, Mar 23 2017

Keywords

Comments

Numbers n such that A054054(n) = 5.
Prime terms are in A106105.

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), this sequence (k = 5), A284067 (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5]
  • Mathematica
    Select[Range[1000], Min[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 23 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 5; \\ Michel Marcus, Mar 25 2017

A284067 Numbers whose smallest decimal digit is 6.

Original entry on oeis.org

6, 66, 67, 68, 69, 76, 86, 96, 666, 667, 668, 669, 676, 677, 678, 679, 686, 687, 688, 689, 696, 697, 698, 699, 766, 767, 768, 769, 776, 786, 796, 866, 867, 868, 869, 876, 886, 896, 966, 967, 968, 969, 976, 986, 996, 6666, 6667, 6668, 6669, 6676, 6677, 6678
Offset: 1

Views

Author

Jaroslav Krizek, Mar 23 2017

Keywords

Comments

Numbers n such that A054054(n) = 6.
Prime terms are in A106106.

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), this sequence (k = 6), A284068 (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 6]
  • Mathematica
    Select[Range[1000], Min[IntegerDigits[#]] == 6 &] (* Giovanni Resta, Mar 23 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 6; \\ Michel Marcus, Mar 25 2017

A284068 Numbers whose smallest decimal digit is 7.

Original entry on oeis.org

7, 77, 78, 79, 87, 97, 777, 778, 779, 787, 788, 789, 797, 798, 799, 877, 878, 879, 887, 897, 977, 978, 979, 987, 997, 7777, 7778, 7779, 7787, 7788, 7789, 7797, 7798, 7799, 7877, 7878, 7879, 7887, 7888, 7889, 7897, 7898, 7899, 7977, 7978, 7979, 7987, 7988, 7989
Offset: 1

Views

Author

Jaroslav Krizek, Mar 23 2017

Keywords

Comments

Numbers n such that A054054(n) = 7.
Prime terms are in A106107.

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), this sequence (k = 7), A284069 (k = 8), A002283 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 7]
  • Mathematica
    Select[Range[8000], Min[IntegerDigits[#]] == 7 &] (* Giovanni Resta, Mar 23 2017 *)
  • PARI
    isok(n) = vecmin(digits(n)) == 7; \\ Michel Marcus, Mar 25 2017

A294069 The smallest digit of a(n+1) is strictly smaller than the largest digit of a(n).

Original entry on oeis.org

1, 10, 20, 11, 30, 2, 12, 13, 14, 3, 15, 4, 16, 5, 17, 6, 18, 7, 19, 8, 21, 31, 22, 40, 23, 24, 25, 26, 27, 28, 29, 32, 41, 33, 42, 34, 35, 36, 37, 38, 39, 43, 50, 44, 51, 45, 46, 47, 48, 49, 52, 53, 54, 60, 55, 61, 56, 57, 58, 59, 62, 63, 64, 65, 70, 66
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Feb 07 2018

Keywords

Comments

The sequence starts with a(1) = 1 and was always extended with the smallest integer not yet present and not leading to a contradiction.
From Robert G. Wilson v, Feb 07 2018: (Start)
Inverse: 1, 6, 10, 12, 14, 16, 18, 20, 2, 4, 7, 8, 9, 11, 13, 15, 17, 19, 3, ..., .
Permutation of the Integers.
(End)

Examples

			The "0" of 10 is strictly < "1", which is the largest digit of 1;
The "0" of 20 is strictly < "1", which is the largest digit of 10;
The "1" of 11 is strictly < "2", which is the largest digit of 20;
The "0" of 30 is strictly < "1", which is the largest digit of 11;
The "2" of 2 is strictly < "3", which is the largest digit of 30;
The "1" of 12 is strictly < "2", which is the largest digit of 2; etc.

Links

Crossrefs

Cf. A002283, A011540, A284062-A284069.

Programs

  • Mathematica
    f[s_List] := Block[{k = 1, mx = Max@IntegerDigits@s[[-1]]}, While[MemberQ[s, k] || Min@IntegerDigits@k >= mx, k++]; Append[s, k]]; Nest[f, {1}, 80] (* Robert G. Wilson v, Feb 07 2018 *)
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.