A244960 -id:A244960 - cp's OEIS frontend

A244954 Smallest positive multiple of n whose base-3 representation contains only 0's and 1's.

1, 4, 3, 4, 10, 12, 28, 40, 9, 10, 121, 12, 13, 28, 30, 112, 85, 36, 247, 40, 84, 352, 253, 120, 325, 364, 27, 28, 841, 30, 31, 256, 363, 850, 280, 36, 37, 760, 39, 40, 82, 84, 3010, 352, 90, 1012, 94, 336, 2548, 850, 255, 364, 742, 108, 2200, 112, 741

Offset: 1

Eric M. Schmidt, Jul 09 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=3)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004283 (written in base 3), A004290, A244955-A244960.

Module[{nn=10,b3},b3=Rest[FromDigits[#,3]&/@Tuples[{0,1},nn]];Table[SelectFirst[b3,Mod[ #,n]==0&],{n,60}]] (* Harvey P. Dale, Feb 01 2024 *)

a(n,b=3) = if (n, k=1; while(vecmax(digits(k*n, b))>1, k++); k*n); \\ Michel Marcus, Jul 10 2014

Data changed, offset changed, Mathematica program replaced, and b-file replaced by Harvey P. Dale, Feb 01 2024

A244955 Smallest positive multiple of n whose base-4 representation contains only 0's and 1's.

Original entry on oeis.org

1, 4, 21, 4, 5, 84, 21, 16, 81, 20, 341, 84, 65, 84, 1365, 16, 17, 324, 1045, 20, 21, 1364, 69, 336, 325, 260, 81, 84, 261, 5460, 341, 64, 1089, 68, 1365, 324, 4181, 4180, 273, 80, 1025, 84, 5461, 1364, 5445, 276, 20821, 336, 1029, 1300, 4437, 260, 5141

Offset: 1

Eric M. Schmidt, Jul 09 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=4)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004284 (written in base 4), A004290, A244954-A244960.

Module[{nn=10,b4},b4=Rest[FromDigits[#,4]&/@Tuples[{0,1},nn]];Table[SelectFirst[b4,Mod[ #,n]==0&],{n,60}]] (* Harvey P. Dale, Feb 01 2024 *)

Data corrected, offset corrected, and b-file replaced by Harvey P. Dale, Feb 01 2024

A244958 Smallest positive multiple of n whose base-7 representation contains only 0's and 1's.

Original entry on oeis.org

1, 8, 57, 8, 50, 19608, 7, 8, 351, 50, 2409, 19608, 351, 56, 2745, 400, 16864, 134856, 57, 400, 399, 2794, 17158, 19608, 50, 19552, 351, 56, 137257, 120450, 16864, 2752, 2409, 16864, 350, 134856, 117993, 19608, 351, 400, 134849, 137256, 344, 16808, 2745

Offset: 1

Eric M. Schmidt, Jul 09 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=7)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004287 (written in base 7), A004290, A244954-A244960.

With[{cl=Rest[{FromDigits[#,7],FromDigits[#]}&/@Tuples[{0,1},7]]},Table[SelectFirst[cl,Mod[ #[[1]],n]==0&],{n,50}]][[;;,1]] (* Harvey P. Dale, Feb 01 2024 *)

Data corrected, Offset corrected, Mathematica program corrected and replaced, and b-file replaced by Harvey P. Dale, Feb 01 2024

A244959 Smallest positive multiple of n whose base 8 representation contains only 0's and 1's.

Original entry on oeis.org

1, 8, 9, 8, 65, 72, 299593, 8, 9, 520, 4169, 72, 65, 2396744, 585, 64, 4097, 72, 513, 520, 17044041, 33352, 33281, 72, 266825, 520, 513, 2396744, 266249, 4680, 4681, 64, 32769, 32776, 16814665, 72, 262145, 4104, 585, 520, 32841, 136352328, 36937, 33352, 585

Offset: 1

Eric M. Schmidt, Jul 09 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=8)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004288 (written in base 8), A004290, A244954-A244960.

Module[{nn=10,b8},b8=Rest[FromDigits[#,8]&/@Tuples[{0,1},nn]];Table[SelectFirst[ b8,Mod[#,n]==0&],{n,100}]] (* Harvey P. Dale, Feb 03 2024 *)

def A244959(n):
    if n > 0:
        for i in range(1,2**n):
            x = int(bin(i)[2:],8)
            if not x % n:
                return x
    return 0 # Chai Wah Wu, Dec 30 2014

Data corrected, offset corrected, and b-file replaced by Harvey P. Dale, Feb 03 2024

A244956 Smallest positive multiple of n whose base-5 representation contains only 0's and 1's.

Original entry on oeis.org

1, 6, 6, 156, 5, 6, 126, 656, 126, 30, 781, 156, 26, 126, 30, 656, 3281, 126, 3781, 780, 126, 3256, 3151, 97656, 25, 26, 756, 756, 15631, 30, 31, 3776, 16401, 3876, 630, 756, 3256, 3876, 156, 3280, 656, 126, 15781, 3256, 630, 16376, 3901, 472656, 15631, 150

Offset: 1

Eric M. Schmidt, Jul 09 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=5)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004285 (written in base 5), A004290, A244954-A244960.

Module[{nn=10,b5},b5=Rest[FromDigits[#,5]&/@Tuples[{0,1},nn]];Table[SelectFirst[b5,Mod[ #,n]==0&],{n,100}]] (* Harvey P. Dale, Feb 01 2024 *)

Data corrected, offset corrected, Mathematica program replaced, and b-file replaced by Harvey P. Dale, Feb 01 2024

A244957 Smallest positive multiple of n whose base-6 representation contains only 0's and 1's.

Original entry on oeis.org

1, 6, 6, 36, 1555, 6, 7, 216, 36, 9330, 253, 36, 1339, 42, 9330, 1296, 1513, 36, 7999, 55980, 42, 1518, 253, 216, 9325, 8034, 216, 252, 47995, 9330, 217, 7776, 1518, 9078, 12093235, 36, 37, 47994, 8034, 335880, 46699, 42, 43, 9108, 55980, 1518, 48175, 1296

Offset: 1

Eric M. Schmidt, Jul 09 2014

Eric M. Schmidt, Table of n, a(n) for n = 0..1000
Ed Pegg Jr., 'Binary' Puzzle
Eric M. Schmidt, Sage code to compute this sequence (use b=6)
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Cf. A004286 (written in base 6), A004290, A244954-A244960.

Module[{nn=10,b6},b6=Rest[FromDigits[#,6]&/@Tuples[{0,1},nn]];Table[SelectFirst[ b6,Mod[#,n]==0&],{n,100}]] (* Harvey P. Dale, Feb 03 2024 *)

Data corrrected, offset corrected, and b-file replaced by Harvey P. Dale, Feb 03 2024

cp's OEIS Frontend

A244954 Smallest positive multiple of n whose base-3 representation contains only 0's and 1's.

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A244955 Smallest positive multiple of n whose base-4 representation contains only 0's and 1's.

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A244958 Smallest positive multiple of n whose base-7 representation contains only 0's and 1's.

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Mathematica

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A244959 Smallest positive multiple of n whose base 8 representation contains only 0's and 1's.

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A244956 Smallest positive multiple of n whose base-5 representation contains only 0's and 1's.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A244957 Smallest positive multiple of n whose base-6 representation contains only 0's and 1's.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions