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 85 results. Next

A198298 Pandigital numbers (A050278) with each product of adjacent digits visible as a substring of the digits.

Original entry on oeis.org

3205486917, 3207154869, 4063297185, 4063792185, 4230567819, 4230915678, 4297630518, 4297631805, 5042976318, 5063297184, 5079246318, 5093271486, 5094236718, 5148609327, 5180429763, 5180792463, 5180942367, 5184063297, 5420796318
Offset: 1

Views

Author

Eric Angelini and Jason Kimberley, Jan 03 2012

Keywords

Comments

There are 58 terms.

Examples

			5x4 ("20") is a substring of 5420976318, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8").
4297631805 is also a member (4*2="8"; 2*9="18"; 9*7="63"; 7*6="42"; 6*3="18"; 3*1="3"; 1*8="8"; 8*0="0"; 0*5="0").

Links

Crossrefs

Cf. A203569, A203566, A210013-A210020.

Programs

  • Python
    from itertools import combinations, permutations
def agen():
    c = 0
    digits = list("0123456789")
    for f in digits[1:]:
        rest = digits[:]
        rest.remove(f)
        for p in permutations(rest):
            t = (f, ) + p
            s = "".join(t)
            if all(str(int(t[i])*int(t[i+1])) in s for i in range(9)):
                yield int(s)
afull = list(agen())
print(afull) # Michael S. Branicky, Oct 03 2024

A210013 Pandigital numbers (A050278) with each product of three adjacent digits visible as a substring of the digits.

Original entry on oeis.org

5631890724, 6581324079, 6581324097, 7249056318
Offset: 1

Views

Author

N. J. A. Sloane, Mar 16 2012

Keywords

Comments

Computed by Jean-Marc Falcoz.

Links

Crossrefs

A generalization of A198298. Cf. A210013-A210020, A203569, A203566.

A257893 Pandigital numbers reordered so that the numbers A050278(n)/2^k, where 2^k||A050278(n), appear in nondecreasing order.

Original entry on oeis.org

3076521984, 3718250496, 6398410752, 1384906752, 2769813504, 2845310976, 1578369024, 1074659328, 4761059328, 9805234176, 2507931648, 1294073856, 5619843072, 6591873024, 9073852416, 9574023168, 1208549376, 1249837056, 6103498752, 1542389760, 1683947520
Offset: 1

Views

Author

Vladimir Shevelev and Peter J. C. Moses, May 12 2015

Keywords

Comments

If two such numbers A050278(n_1)/2^k_1 and A050278(n_2)/2^k_2 are equal, then A050278(n_1) appears earlier than A050278(n_2) iff A050278(n_1)<A050278(n_2). For example, a(4)/2^18=a(5)/2^19=5283.
There are 184423 such pairs.

Links

Crossrefs

Cf. A050278.

Programs

  • Python
    from itertools import permutations
l = []
for d in permutations('0123456789', 10):
    if d[0] != '0':
        d2 = int(''.join(d))
        d = d2
        r = d2 % 2
        while not r:
            d2, r = divmod(d2, 2)
        l.append((d2,d))
l.sort()
A257893_list = [b for a,b in l] # Chai Wah Wu, May 24 2015

Formula

min(A050278(n)/2^k) = 3076521984/2^21 = 1467.

A257899 Pandigital numbers reordered so that the numbers A050278(n)/3^k, where 3^k||A050278(n), are in nondecreasing order.

Original entry on oeis.org

7246198035, 3410256897, 5361708249, 5902183746, 6820513794, 8145396207, 8269753401, 9145036728, 9537240186, 1257389406, 1359426078, 4379605281, 1742063598, 6185973240, 2081654397, 2095471863, 6472951380, 2170936485, 2304859617, 2415930786, 2419650873
Offset: 1

Views

Author

Vladimir Shevelev and Peter J. C. Moses, May 12 2015

Keywords

Comments

If two such numbers A050278(n_1)/3^k_1 and A050278(n_2)/3^k_2 are equal, then A050278(n_1) appears earlier than A050278(n_2) iff A050278(n_1)<A050278(n_2).
There are 5985 such pairs.

Links

Crossrefs

Cf. A050278, A257893.

Programs

  • Python
    from itertools import permutations
l = []
for d in permutations('0123456789', 10):
    if d[0] != '0':
        d2 = int(''.join(d))
        d = d2
        r = d2 % 3
        while not r:
            d2, r = divmod(d2, 3)
        l.append((d2,d))
l.sort()
A257899_list = [b for a,b in l] # Chai Wah Wu, May 24 2015

Formula

min(A050278(n)/3^k) = 7246198035/3^15 = 505

A203987 Number of integers m such that both m and n*m are decimal pandigital numbers (A050278).

Original entry on oeis.org

3265920, 184320, 5820, 6480, 46080, 998, 387, 171, 167
Offset: 1

Views

Author

Zak Seidov, Jan 09 2012

Keywords

Comments

a(1) = 3265920 = 9*9! is trivially the number of all terms in A050278.

Crossrefs

Cf. A050278.

A257901 Pandigital numbers reordered so that the numbers A050278(n)/5^k, where 5^k||A050278(n), are in nondecreasing order.

Original entry on oeis.org

1304296875, 1342968750, 1437890625, 1824609375, 9123046875, 1923046875, 3104296875, 3142968750, 3649218750, 4137890625, 4862109375, 1034296875, 1269843750, 6349218750, 1284609375, 1293046875, 1347890625, 1432968750, 8124609375, 1629843750, 8462109375
Offset: 1

Views

Author

Vladimir Shevelev and Peter J. C. Moses, May 12 2015

Keywords

Comments

If two such numbers A050278(n_1)/5^k_1 and A050278(n_2)/5^k_2 are equal, then A050278(n_1) appears earlier than A050278(n_2) iff A050278(n_1)<A050278(n_2). For example, a(4)/5^8=a(5)/5^9=4671.
There are 46080 such pairs.

Links

Crossrefs

Cf. A050278, A257893, A257899.

Programs

  • Python
    from itertools import permutations
l = []
for d in permutations('0123456789', 10):
    if d[0] != '0':
        d2 = int(''.join(d))
        d = d2
        r = d2 % 5
        while not r:
            d2, r = divmod(d2,5)
        l.append((d2,d))
l.sort()
A257901_list = [b for a,b in l] # Chai Wah Wu, May 24 2015

Formula

min(A050278(n)/5^k) = 1304296875/5^8 = 3339.

A204045 Smallest integer m such that both m and n*m are decimal pandigital numbers (A050278).

Original entry on oeis.org

1023456789, 1023456789, 1023748965, 1023456789, 1024693578, 1023465897, 1023547986, 1023794658, 1023674985
Offset: 1

Views

Author

Zak Seidov, Jan 09 2012

Keywords

Comments

Corresponding indices of a(n) in A050278 are 1, 1, 378, 1, 1057, 28, 132, 459, 294.
Note that a(1)=a(2)=a(4)=A050278(1).

Crossrefs

Cf. A050278, A203987.

A318787 Primes that divide exactly one pandigital number (A050278 - each digit 0-9 appears exactly once, no leading zero).

Original entry on oeis.org

293339, 318743, 327661, 344479, 345533, 355559, 367789, 382813, 386549, 393373, 395491, 395537, 395677, 398129, 404321, 405989, 406649, 407807, 409901, 410413, 421469, 425813, 426161, 426487, 429971, 430259, 430847, 432337, 432983, 434563, 435839, 438499, 439991, 440311, 441613, 443089
Offset: 1

Views

Author

Jud McCranie, Sep 03 2018

Keywords

Comments

The corresponding pandigital numbers are in A318788.
The last term is a(834218) = 1097393447, which divides 9876541023. - Giovanni Resta, Sep 04 2018

Examples

			293339 is prime and 1795234680 is the only pandigitial number that it divides.

Links

Crossrefs

Cf. A050278, A318788.

A071924 Highest m such that prime(m) divides the n-th pandigital (A050278).

Original entry on oeis.org

749, 208, 6503705, 1831, 657, 1045880, 6503711, 239879, 375325, 7864, 45075, 7064, 2313602, 6503717, 59, 1766468, 78975, 840, 1046, 33355, 2133, 109, 107390, 56057, 6503758, 3386573, 6503759, 2044, 3386575, 158964, 2313623, 9463, 2313625, 36081
Offset: 1

Views

Author

Lekraj Beedassy, Jun 14 2002

Keywords

Examples

			The 10th pandigital 1023457896 has prime decomposition 2^3*3^3*59*80309 and 80309 is indeed the a(10)=7864th prime, i.e., prime(7864)=80309.

Links

Crossrefs

Cf. A050278.

Programs

  • Mathematica
    PrimePi[FactorInteger[#][[-1,1]]]&/@(Select[Sort[FromDigits/@ Permutations[ Range[0,9]]],IntegerLength[#]>9&,50]) (* Harvey P. Dale, Jun 06 2018 *)
  • Python
    from itertools import permutations, islice
from sympy import primepi, primefactors
def A071924(n): return primepi(max(primefactors(next(islice((int(e+''.join(d)) for e in '123456789' for d in permutations('0123456789'.replace(e,''),9)),n-1,None))))) # Chai Wah Wu, Dec 07 2021

Extensions

a(24)-a(33) from Donovan Johnson, Jan 25 2009
Edited by Charles R Greathouse IV, Aug 02 2010
Keyword "fini" added by Sean A. Irvine, Aug 21 2024

A071926 Least m such that m-th pandigital A050278(m) is a multiple of n or -1 if no such m exists.

Original entry on oeis.org

1, 2, 1, 10, 34, 2, 2, 10, 1, 46234, 771, 10, 2, 2, 34, 11, 8, 2, 15, 46236, 2, 773, 49, 10, 42, 2, 1, 62, 41, 46234, 15, 18, 771, 8, 58, 10, 270, 50, 2, 46266, 15, 2, 48, 773, 34, 52, 35, 11, 71, 46386, 8, 11, 22, 5, 2238, 71, 15, 69, 10, 46236, 18, 102, 2, 53, 46, 773, 75
Offset: 1

Views

Author

Lekraj Beedassy, Jun 14 2002

Keywords

Comments

The first escape term is a(100) = -1. - Georg Fischer, Feb 19 2019

Links

Crossrefs

Cf. A050278.

Formula

a(n) = -1 for n > 9876543210. - Sean A. Irvine, Aug 22 2024

Extensions

More terms from Sascha Kurz, Feb 07 2003
Edited by Charles R Greathouse IV, Aug 02 2010
Escape clause added to definition by Chai Wah Wu, Oct 12 2017
Showing 1-10 of 85 results. Next

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

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