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 13 results. Next

A003635 Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10).

Original entry on oeis.org

62, 63, 65, 75, 84, 95, 161, 173, 195, 216, 261, 266, 272, 276, 326, 371, 372, 377, 381, 383, 386, 387, 395, 411, 416, 422, 426, 431, 432, 438, 441, 443, 461, 466, 471, 476, 482, 483, 486, 488, 491, 492, 493, 494, 497, 498, 516, 521, 522, 527, 531, 533, 536
Offset: 1

Views

Author

N. J. A. Sloane and Mira Bernstein

Keywords

References

  • J. H. Conway, personal communication.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A003634, A052489, A052490, A052491, A058898-A058917.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    nmax = 1000; Reap[ Do[k = n; kmax = 100*n; While[ Tr[ IntegerDigits[k]]*n != k && k < kmax, k = k + n]; If[k == kmax, Sow[n]], {n, 1, nmax}]][[2, 1]] (* Jean-François Alcover, Jul 12 2012 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
def A003635_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 9*l*n < 10**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(10),l):
                if (s:=sum(d))>0 and sorted(str(s*n)) == [str(e) for e in d]:
                    break
            else:
                continue
            break
A003635_list = list(islice(A003635_gen(),20)) # Chai Wah Wu, May 09 2023

A058898 Inconsummate numbers in base 2: no number is this multiple of the sum of its digits (in base 2).

Original entry on oeis.org

13, 19, 25, 26, 35, 38, 47, 49, 50, 52, 55, 67, 70, 76, 94, 95, 97, 98, 100, 103, 104, 109, 110, 115, 117, 131, 134, 140, 151, 152, 157, 159, 171, 175, 179, 183, 185, 187, 188, 190, 193, 194, 196, 199, 200, 203, 206, 208, 217, 218, 220, 227, 229
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Comments

Equivalently, these are the natural numbers that cannot be written as the arithmetic mean of distinct powers of 2. - Brian Kell, Feb 28 2009

Links

Crossrefs

Cf. A003635, A052491, A058899-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    Do[k = n; While[ Apply[ Plus, IntegerDigits[k, 2] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]
  • Python
    from itertools import count, islice, combinations_with_replacement
def A058898_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if l*n < 1<0 and sorted(bin(s*n)[2:]) == [str(e) for e in d]:
                    break
            else:
                continue
            break
A058898_list = list(islice(A058898_gen(),20)) # Chai Wah Wu, May 09 2023

Formula

n such that A065413(n) = 0. - Brian Kell, Mar 01 2009

A058907 Inconsummate numbers in base 12: no number is this multiple of the sum of its digits (in base 12).

Original entry on oeis.org

86, 87, 88, 90, 99, 101, 102, 112, 113, 114, 125, 126, 138, 229, 235, 244, 245, 246, 256, 258, 269, 270, 282, 307, 373, 379, 385, 391, 392, 400, 402, 426, 451, 464, 530, 535, 536, 542, 543, 547, 548, 607, 608, 620, 667, 673, 674, 679, 680, 685
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898, A058899, A058900, A058901, A058902, A058903, A058904, A058905, A058906.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=12; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Sep 23 2017; after N. J. A. Sloane in A058906 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058907_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 11*l*n < 12**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(12),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,12)[1:]) == list(d):
                    break
            else:
                continue
            break
A058907_list = list(islice(A058907_gen(),20)) # Chai Wah Wu, May 10 2023

A058906 Inconsummate numbers in base 11: no number is this multiple of the sum of its digits (in base 11).

Original entry on oeis.org

68, 70, 79, 80, 82, 92, 104, 200, 202, 212, 214, 224, 225, 248, 260, 314, 320, 332, 380, 392, 452, 458, 464, 490, 502, 508, 512, 513, 514, 518, 520, 524, 530, 562, 568, 574, 578, 579, 580, 584, 585, 590, 592, 595, 598, 599, 622, 628, 634, 635
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    digitsum := proc (n,b) local i; add(i,i=convert(n,base,b)) end; b := 11:N := 43922; L := []: for n from 1 to N do k := digitsum(n,b): if (n mod k)=0 then L := [op(L), n/k] fi: od: M := []: for i from 1 to 1000 do if not(member(i,L)) then M := [op(M),i] fi od: lprint(M);
  • Mathematica
    base = 11; Do[k = n; While[ Apply[ Plus, IntegerDigits[k, base] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058906_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 10*l*n < 11**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(11),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,11)[1:]) == list(d):
                    break
            else:
                continue
            break
A058906_list = list(islice(A058906_gen(),20)) # Chai Wah Wu, May 09 2023

A058899 Inconsummate numbers in base 3: no number is this multiple of the sum of its digits (in base 3).

Original entry on oeis.org

17, 32, 44, 51, 94, 95, 96, 106, 107, 112, 118, 132, 148, 153, 199, 224, 226, 232, 235, 236, 238, 256, 265, 268, 269, 274, 277, 281, 282, 284, 285, 288, 296, 308, 318, 321, 334, 336, 343, 352, 354, 368, 396, 442, 443, 444, 454, 459, 469, 472
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=3; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250 n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Sep 23 2017 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058899_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 2*l*n < 3**(l-1):
                yield n
                break
            for d in combinations_with_replacement((0,1,2),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,3)[1:]) == list(d):
                    break
            else:
                continue
            break
A058899_list = list(islice(A058899_gen(),20)) # Chai Wah Wu, May 10 2023

A058900 Inconsummate numbers in base 4: no number is this multiple of the sum of its digits (in base 4).

Original entry on oeis.org

29, 41, 71, 83, 93, 111, 113, 114, 116, 117, 122, 123, 125, 135, 137, 143, 146, 153, 164, 167, 191, 197, 201, 237, 242, 263, 275, 279, 282, 284, 285, 291, 303, 305, 311, 323, 326, 327, 332, 359, 362, 369, 372, 375, 377, 382, 383, 389, 407, 410
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058900_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 3*l*n < 1<<((l-1)<<1):
                yield n
                break
            for d in combinations_with_replacement((0,1,2,3),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,4)[1:]) == list(d):
                    break
            else:
                continue
            break
A058900_list = list(islice(A058900_gen(),20)) # Chai Wah Wu, May 10 2023

A058901 Inconsummate numbers in base 5: no number is this multiple of the sum of its digits (in base 5).

Original entry on oeis.org

16, 22, 28, 46, 56, 58, 68, 74, 76, 80, 106, 108, 110, 118, 128, 136, 138, 140, 146, 152, 168, 198, 202, 206, 208, 230, 249, 256, 258, 262, 263, 268, 274, 276, 278, 280, 284, 286, 288, 290, 292, 294, 296, 298, 302, 318, 323, 324, 326, 336, 338
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=5; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^4}] (* Vincenzo Librandi, Nov 03 2016 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058901_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 4*l*n < 5**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(5),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,5)[1:]) == list(d):
                    break
            else:
                continue
            break
A058901_list = list(islice(A058901_gen(),20)) # Chai Wah Wu, May 10 2023

A058902 Inconsummate numbers in base 6: no number is this multiple of the sum of its digits (in base 6).

Original entry on oeis.org

27, 33, 64, 82, 97, 100, 103, 104, 107, 118, 122, 124, 125, 128, 134, 135, 152, 159, 162, 177, 190, 193, 195, 198, 205, 208, 212, 214, 232, 233, 250, 277, 280, 298, 334, 343, 345, 349, 352, 358, 362, 363, 364, 370, 380, 382, 384, 403, 427, 442
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=6; Do[k=n; While[Apply[Plus,IntegerDigits[k, base]] n!=k&&k<250 n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Jan 30 2017 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058902_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 5*l*n < 6**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(6),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,6)[1:]) == list(d):
                    break
            else:
                continue
            break
A058902_list = list(islice(A058902_gen(),20)) # Chai Wah Wu, May 10 2023

A058903 Inconsummate numbers in base 7: no number is this multiple of the sum of its digits (in base 7).

Original entry on oeis.org

30, 86, 102, 134, 138, 141, 158, 162, 167, 170, 183, 186, 194, 210, 213, 233, 284, 290, 306, 312, 314, 326, 330, 338, 354, 362, 366, 368, 428, 452, 480, 530, 534, 536, 540, 542, 554, 564, 578, 591, 602, 645, 648, 656, 705, 708, 714, 740, 746
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Links

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=7; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Jan 30 2017 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058903_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 6*l*n < 7**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(7),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,7)[1:]) == list(d):
                    break
            else:
                continue
            break
A058903_list = list(islice(A058903_gen(),20)) # Chai Wah Wu, May 10 2023

A058904 Inconsummate numbers in base 8: no number is this multiple of the sum of its digits (in base 8).

Original entry on oeis.org

42, 44, 51, 52, 60, 105, 109, 116, 124, 173, 177, 178, 181, 201, 205, 209, 210, 213, 214, 217, 233, 237, 241, 242, 245, 249, 250, 251, 254, 255, 269, 273, 277, 278, 282, 285, 287, 290, 298, 299, 300, 308, 336, 343, 348, 352, 397, 401, 402, 403
Offset: 1

Views

Author

N. J. A. Sloane, Jan 09 2001

Keywords

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

  • Maple
    For Maple code see A058906.
  • Mathematica
    base=8; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Sep 21 2017 *)
  • Python
    from itertools import count, islice, combinations_with_replacement
def A058904_gen(startvalue=1): # generator of terms
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 7*l*n < 1<<3*(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(8),l):
                if (s:=sum(d)) > 0 and sorted(oct(s*n)[2:]) == list(map(str,d)):
                    break
            else:
                continue
            break
A058904_list = list(islice(A058904_gen(),20)) # Chai Wah Wu, May 09 2023
Showing 1-10 of 13 results. Next

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

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