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.

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A171397 Write n in base 10, but then read it as if it were written in base 11: if n = Sum_{i >= 0} d_i*10^i, with 0 <= d_i <= 9, then a(n) = Sum_{i >= 0} d_i*11^i.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72
Offset: 0

Views

Author

Paul Weisenhorn, Jul 11 2011

Keywords

Comments

This is the sequence of all decimal integers that are created when base 10 numbers are interpreted as base 11 numbers.
Numbers without digit A (=10) in their representation in base 11. Complement of A095778. - François Marques, Oct 20 2020
Original definition: Earliest sequence containing no 11-term arithmetic progression.
In general, if p is prime, the earliest sequence containing no p-term arithmetic progression is created when base (p-1) numbers are interpreted as base p numbers.

Examples

			a(53)=58 because 53_11 in base 11 equals 58. - _François Marques_, Oct 20 2020

References

  • D. E. Arganbright, Mathematical Modeling with Spreadsheets, ABACUS, Vol. 3, #4(1986), 19-31.

Links

Crossrefs

Different from A065039. - Alois P. Heinz, Sep 07 2011
CNumbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Numbers with no digit b-1 in base b : A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), this sequence (b=11).

Programs

  • Maple
    seq(`if`(numboccur (10, convert (n, base, 11))=0, n, NULL), n=0..122);
# second Maple program:
a:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(n, base, 10)):
seq(a(n), n=0..66);  # Alois P. Heinz, Aug 30 2024
  • Mathematica
    Table[FromDigits[RealDigits[n, 10], 11], {n, 0, 100}] (* François Marques, Oct 20 2020 *)
  • PARI
    a(n) = fromdigits(digits(n), 11); \\ Michel Marcus, Oct 09 2020
  • Python
    def A171397(n): return int(str(n),11) # Chai Wah Wu, Aug 30 2024

Extensions

Edited by N. J. A. Sloane, Aug 31 2024

A037465 a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*5^i is the base 5 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93
Offset: 0

Views

Author

Clark Kimberling

Keywords

Comments

Numbers without digit 5 in base 6. Complement of A333656. - François Marques, Oct 13 2020

Examples

			a(34)=46 because 34 is 114_5 in base 5 and 114_6=46. - _François Marques_, Oct 13 2020

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), this sequence (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Mathematica
    Table[FromDigits[RealDigits[n, 5], 6], {n, 0, 100}] (* Clark Kimberling, Aug 14 2012 *)
  • PARI
    a(n) = fromdigits(digits(n, 5), 6); \\ François Marques, Oct 13 2020
  • Python
    from gmpy2 import digits
def A037465(n): return int(digits(n,5),6) # Chai Wah Wu, May 06 2025

Extensions

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A338090 Numbers having at least one 8 in their representation in base 9.

Original entry on oeis.org

8, 17, 26, 35, 44, 53, 62, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 89, 98, 107, 116, 125, 134, 143, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 170, 179, 188, 197, 206, 215, 224, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 251, 260, 269, 278, 287, 296, 305, 314, 315
Offset: 1

Views

Author

François Marques, Oct 09 2020

Keywords

Comments

Blocks of consecutive terms have lengths in A002452. - Devansh Singh, Oct 21 2020

Examples

			70 is not in the sequence since it is 77_9 in base 9, but 76 is in the sequence since it is 84_9 in base 9.

Links

Crossrefs

Cf. A007095 (base 9).
Complement of A037477.
Cf. A043485 (numbers with exactly one 8 in base 9).
Cf. Numbers with at least one digit b-1 in base b: A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), this sequence (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(8, convert(n, base, 9))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 9 ], 8 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==8), digits(m, 9)) >= 1;
  • Python
    from gmpy2 import digits
def A338090(n):
    def f(x):
        l = (s:=digits(x,9)).find('8')
        if l >= 0: s = s[:l]+'7'*(len(s)-l)
        return n+int(s,8)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A037474 a(n) = Sum{d(i)*8^i: i=0,1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is the base 7 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85
Offset: 0

Views

Author

Clark Kimberling

Keywords

Comments

Numbers without digit 7 in base 8. Complement of A337239. - François Marques, Oct 13 2020

Examples

			a(48)=54 because 48 is 66_7 in base 7 and 66_8=54. - _François Marques_, Oct 13 2020

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), this sequence (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Mathematica
    Table[FromDigits[RealDigits[n, 7], 8], {n, 0, 100}] (* Clark Kimberling, Aug 14 2012 *)
  • PARI
    a(n) = fromdigits(digits(n, 7), 8); \\ François Marques, Oct 13 2020
  • Python
    from gmpy2 import digits
def A037474(n): return int(digits(n,7),8) # Chai Wah Wu, Dec 04 2024

Extensions

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A037477 a(n) = Sum{d(i)*9^i: i=0,1,...,m}, where Sum{d(i)*8^i: i=0,1,...,m} is the base 8 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 81, 82, 83, 84, 85
Offset: 0

Views

Author

Clark Kimberling

Keywords

Comments

Numbers that do not contain the digit 8 in their base 9 expansion. - M. F. Hasler, Oct 05 2014

Examples

			a(63) = 7*9+7 = 70 since 63 = 77[8], i.e., "77" when written in base 8;
a(64) = 1*9^2 = 81 since 64 = 100[8]. - _M. F. Hasler_, Oct 05 2014

Links

Crossrefs

Cf. A248375.
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), this sequence (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Mathematica
    Table[FromDigits[RealDigits[n, 8], 9], {n, 0, 100}]
Select[Range[0,100],DigitCount[#,9,8]==0&] (* Harvey P. Dale, Aug 06 2024 *)
  • PARI
    a(n) = vector(#n=digits(n,8),i,9^(#n-i))*n~ \\ M. F. Hasler, Oct 05 2014
  • PARI
    a(n) = fromdigits(digits(n, 8), 9); \\ François Marques, Oct 15 2020
  • Python
    def A037477(n): return int(oct(n)[2:],9) # Chai Wah Wu, Jan 27 2025

Formula

For n<64, a(n) = floor(9n/8) = A248375(n). - M. F. Hasler, Oct 05 2014

Extensions

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A095778 Values of n for which A095777(n) is 9 (those terms which are expressible in decimal digits for bases 2 through 10, but not for base 11).

Original entry on oeis.org

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 352, 353
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jun 05 2004

Keywords

Comments

Numbers with at least one digit A (=10) in their representation in base 11. Complementary sequence to A171397. - François Marques, Oct 11 2020

Examples

			a(5)=54 because 54 when expressed in successive bases starting at 2 will produce its first non-decimal digit at base 11. Like so: 110110, 2000, 312, 204, 130, 105, 66, 60, 54. In base 11, 54 is 4A.

Links

Crossrefs

Cf. A095777.
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), this sequence (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    S := []; for n from 1 to 1000 do; if 1>0 then; ct := 0; ok := true; b := 2; if (n>9) then; while ok=true do; L := convert(n, base, b); for e in L while ok=true do; if (e > 9) then ok:=false; fi; od; if ok=true then; ct := ct + 1; b := b + 1; fi; od; fi; if ct=9 then S := [op(S), n]; fi; fi; od; S;
# or
seq(`if`(numboccur(10, convert(n, base, 11))>0, n, NULL), n=0..1000); # François Marques, Oct 11 2020
  • Mathematica
    Select[Range[400],Max[IntegerDigits[#,11]]>9&] (* Harvey P. Dale, Sep 30 2018 *)
  • PARI
    isok(m) = #select(x->(x==10), digits(m, 11)) >= 1; \\ François Marques, Oct 11 2020
  • Python
    from gmpy2 import digits
def A095778(n):
    def f(x):
        l = (s:=digits(x,11)).find('a')
        if l >= 0: s = s[:l]+'9'*(len(s)-l)
        return n+int(s)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A293869 Square array whose n-th row lists all numbers having n as a substring, n >= 1; read by falling antidiagonals.

Original entry on oeis.org

1, 10, 2, 11, 12, 3, 12, 20, 13, 4, 13, 21, 23, 14, 5, 14, 22, 30, 24, 15, 6, 15, 23, 31, 34, 25, 16, 7, 16, 24, 32, 40, 35, 26, 17, 8, 17, 25, 33, 41, 45, 36, 27, 18, 9, 18, 26, 34, 42, 50, 46, 37, 28, 19, 10, 19, 27, 35, 43, 51, 56, 47, 38, 29, 100, 11
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Examples

			The array starts:
   [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531
   [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532
   [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533
   [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534
   [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535
   [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536
   [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537
   [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538
   [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539
   [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
   [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
   [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
   [   ...             ...             ...             ...]

Links

Crossrefs

Cf. A072484, A292690 (variant starting with row 0).
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539, A293870, A293871, A293872.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.
Cf. A179239, A261370.
Cf. A292451, A292731 (both partially coincide with row 11, but no inclusion relation holds).

Programs

  • Mathematica
    Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n+1], {n, d}]; Table[a[[n, k-n+1]], {k, d}, {n, k}]] (* Paolo Xausa, Mar 01 2024 *)
  • PARI
    has=(n,p,m=10^#Str(p))->until(p>n\=10,n%m==p&&return(1))
Mat(vectorv(12,n,a=[];for(k=n,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
  • Perl
    See Links section.

Formula

T(n, k) = A072484(n, k) for any n > 0 and k = 1..n. - Rémy Sigrist, Jan 29 2021

A337250 Numbers having at least one 3 in their representation in base 4.

Original entry on oeis.org

3, 7, 11, 12, 13, 14, 15, 19, 23, 27, 28, 29, 30, 31, 35, 39, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 71, 75, 76, 77, 78, 79, 83, 87, 91, 92, 93, 94, 95, 99, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119
Offset: 1

Views

Author

François Marques, Sep 19 2020

Keywords

Comments

Complementary sequence of A023717.

Examples

			18 is not in the sequence since it is 102_4 in base 4, but 19 is in the sequence since it is 103_4 in base 4.

Links

Crossrefs

Cf. A196032 (at least one 0 in base 4).
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), this sequence, A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(3, convert(n, base, 4))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 4 ], 3 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==3), digits(m, 4)) >= 1; \\ Michel Marcus, Sep 20 2020
  • Python
    from gmpy2 import digits
def A337250(n):
    def f(x):
        l = (s:=digits(x,4)).find('3')
        if l >= 0: s = s[:l]+'2'*(len(s)-l)
        return n+int(s,3)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A337572 Numbers having at least one 4 in their representation in base 5.

Original entry on oeis.org

4, 9, 14, 19, 20, 21, 22, 23, 24, 29, 34, 39, 44, 45, 46, 47, 48, 49, 54, 59, 64, 69, 70, 71, 72, 73, 74, 79, 84, 89, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 129, 134
Offset: 1

Views

Author

François Marques, Sep 19 2020

Keywords

Comments

Complementary sequence to A020654.

Examples

			75 is not in the sequence since it is 300_5 in base 5, but 74 is in the sequence since it is 244_5 in base 5.

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), this sequence (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(4, convert(n, base, 5))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 5 ], 4 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==4), digits(m, 5)) >= 1; \\ Michel Marcus, Sep 20 2020
  • Python
    from gmpy2 import digits
def A337572(n):
    def f(x):
        l = (s:=digits(x,5)).find('4')
        if l >= 0: s = s[:l]+'3'*(len(s)-l)
        return n+int(s,4)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A292690 Square array whose n-th row lists all numbers having n as a substring, read by falling antidiagonals, n >= 0.

Original entry on oeis.org

0, 10, 1, 20, 10, 2, 30, 11, 12, 3, 40, 12, 20, 13, 4, 50, 13, 21, 23, 14, 5, 60, 14, 22, 30, 24, 15, 6, 70, 15, 23, 31, 34, 25, 16, 7, 80, 16, 24, 32, 40, 35, 26, 17, 8, 90, 17, 25, 33, 41, 45, 36, 27, 18, 9, 100, 18, 26, 34, 42, 50, 46, 37, 28, 19, 10
Offset: 0

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

This array starts with row 0, see A293869 for the variant which starts with row 1.

Examples

			The array starts:
   [ 0  10  20  30  40  50  60  70  80  90 100 101 102 ...] = A011540
   [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531
   [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532
   [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533
   [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534
   [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535
   [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536
   [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537
   [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538
   [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539
   [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
   [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
   [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
   [   ...             ...             ...             ...]

Links

Crossrefs

Cf. A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: rows 0 - 9.
Cf. A293870, A293871, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: rows 10 .. 20.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, only multiples of the pattern p.

Programs

  • Mathematica
    Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n], {n, 0, d-1}]; Table[a[[n+1, k-n]], {k, d}, {n, 0, k-1}]] (* Paolo Xausa, Mar 01 2024 *)
  • PARI
    has(n,p,m=10^#Str(p))=until(p+!p>n\=10,n%m==p&&return(1))
Mat(vectorv(12,n,a=[];for(k=n--,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
for(i=1,11,for(j=1,i,print1(%[j,i-j+1]","))) \\ Read by antidiagonals
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