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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A048937 Numbers n with an even number of digits, n = d_1 d_2 ... d_n, such that there are exactly three ways to partition the digits into two groups of size n/2, say f_1 ... f_{n/2} and g_1 ... g_{n/2}, such that n = f_1 ... f_{n/2} * g_1 ... g_{n/2}.

Original entry on oeis.org

13078260, 107650322640, 113024597400, 119634515208, 134549287600, 135173486250, 138130447950, 146083269717, 150967233648, 216315684000, 221089445500, 315987404670, 463997983680, 472812953760, 10174695862032, 10178463985200, 10185571893960, 10476754939728, 10624657891320
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

f_{n/2} and g_{n/2} may not both be zero.
Vampire numbers (definition 2) having exactly three distinct pairs of fangs.

Examples

			13078260 = 1620*8073 = 1863*7020 = 2070*6318; 107650322640 = 153204*702660 = 140532*766020 = 200760*536214.

References

  • C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to Infinity. New York: Wiley, pp. 227-231, 1995.

Links

Crossrefs

Cf. A014575, A048933, ..., A048939.

Extensions

More terms found by Walter Schneider, Feb 11 2002 and communicated by Hans Havermann, Oct 10 2002
More terms from Jens Kruse Andersen, Dec 01 2002

A053652 Primes for which some rearrangement of the digits (leading zeros not allowed) is the product of two consecutive primes.

Original entry on oeis.org

53, 233, 347, 431, 743, 1237, 1249, 1327, 1367, 1429, 1471, 1571, 1583, 1637, 1723, 1741, 2137, 2371, 2713, 2731, 3167, 3217, 3271, 3581, 3617, 3671, 3761, 3851, 3863, 3877, 4129, 4219, 5171, 5381, 5399, 5477, 5657, 5711, 5813, 5939
Offset: 1

Views

Author

Enoch Haga, Feb 18 2000

Keywords

Comments

Primes from A053736 sorted in numerical order.

Examples

			a(3)=347, a(5)=743. These terms are derived from 19*23=437. By arranging digits of 437, two primes are formed: 347 and 743.

References

  • C. A. Pickover, "Vampire numbers," chapter 30 of Keys to Infinity. NY: Wiley, 1995. Pages 227-231

Crossrefs

Cf. A053736, A053653, A014575.

Extensions

Edited by Jens Kruse Andersen, Dec 01 2006

A053736 Run through primes p; if the digits of p*q (where q is the prime following p) can be rearranged to form one or more primes r, append these primes r to the sequence.

Original entry on oeis.org

53, 431, 233, 347, 743, 1471, 1741, 7411, 1571, 5171, 5711, 7151, 1367, 1637, 3167, 3617, 3671, 3761, 6173, 6317, 1249, 1429, 4129, 4219, 9241, 9421, 1237, 1327, 1723, 2137, 2371, 2713, 2731, 3217, 3271, 7213, 7321, 5399, 5939, 9539
Offset: 1

Views

Author

Enoch Haga, Feb 13 2000

Keywords

Comments

Leading zeros are not allowed in the rearranged number.

Examples

			7*11=77, but no prime rearrangements are possible; 11*13 is 143, whose digits can be rearranged to 431, a prime.

References

  • C. A. Pickover, "Vampire numbers," chapter 30 of Keys to Infinity. NY: Wiley, 1995. Pages 227-231

Crossrefs

A053652 gives the entries sorted and with duplicates removed. Cf. A014575, A053652.

Extensions

Corrected and extended by Jens Kruse Andersen, Dec 01 2006

A048935 Number of distinct vampire numbers (definition 2) having 2n digits.

Original entry on oeis.org

0, 7, 148, 3228, 108454, 4390670, 208423682, 11039126154
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

  • C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to Infinity. New York: Wiley, pp. 227-231, 1995.

Links

Crossrefs

Cf. A014575, A048938, A048939.

Extensions

More terms from Jens Kruse Andersen, Dec 01 2002
a(8) from Pierro Zachareas, Mar 11 2021
a(8) corrected by Pierro Zachareas, Jul 03 2022

A289911 Prime vampire numbers: semiprimes x*y such that x and y have the same number of digits and the union of the multisets of the digits of x and y is the same as the multiset of digits of x*y.

Original entry on oeis.org

117067, 124483, 146137, 371893, 536539, 10349527, 10429753, 10687513, 11722657, 11823997, 12451927, 12484057, 12894547, 13042849, 14145799, 14823463, 17204359, 18517351, 18524749, 18647023, 19262587, 19544341, 19554277, 20540911, 20701957, 21874387, 30189721
Offset: 1

Views

Author

Felix Fröhlich, Jul 15 2017

Keywords

Comments

Subsequence of A014575.

Examples

			117067 = 167 * 701. A055642(117067) mod 2 = 0, A055642(167) = A055642(701) and the multiset of digits of 117067 is {0, 1, 1, 6, 7, 7}, which is also the multiset resulting from the union of the multisets of digits of 167 and 701, so 117067 is a term of the sequence.

Links

Crossrefs

Cf. A001358, A001637, A014575, A055642.

Programs

  • PARI
    is_a001637(n) = #Str(n)%2==0
is_a001358(n) = omega(n)==2
samefactorlength(v) = #Str(v[1])==#Str(v[2])
samedigitmultiset(v) = vecsort(concat(digits(v[1]), digits(v[2])))==vecsort(digits(v[1]*v[2]))
is(n) = if(!is_a001637(n) || !is_a001358(n) || (!issquarefree(n) && bigomega(n) > 2), return(0), my(f=factor(n)[, 1]~); if(samefactorlength(f) && samedigitmultiset(f), return(1), return(0)))
  • PARI
    \\ terms with n digits (if n is odd then returns terms with n + 1 digits).
ndigits(n) = {n-=2; n+=(n%2); my(res=List()); forprime(p=ceil(10^(n/2)), 10^(n/2+1)-1, forprime(q = max(p, ceil(10^(n+1)/p)), 10^(n/2+1)-1, if(Set(vecsort(digits(p*q)) -vecsort(concat(digits(p),digits(q))))==[0], listput(res, p*q)))); listsort(res); res} \\ David A. Corneth, Jul 24 2017

A094208 Least vampire number with n fang pairs.

Original entry on oeis.org

1260, 125460, 13078260, 16758243290880, 24959017348650
Offset: 1

Views

Author

Lekraj Beedassy, May 27 2004

Keywords

Examples

			a(2) is the smallest number which can be written in 2 ways as the product of two numbers with half as many digits and not both ending in 0: 125460 = 204*615 = 246*510. - _Jens Kruse Andersen_, Jun 14 2014

Links

Crossrefs

Cf. A020342, A014575, A048936, A048937.

Extensions

Typo in Cf. to A014575 fixed by Jens Kruse Andersen, Jun 14 2014

A167266 Vampire numbers permutations of whose digits are other vampire numbers.

Original entry on oeis.org

1827, 2187, 102510, 105210, 105264, 115672, 116725, 123354, 125248, 125433, 125460, 126846, 129775, 133245, 134725, 152608, 153436, 156240, 156289, 174370, 175329, 180225, 182250, 182650, 186624, 193257, 197725, 201852, 215860, 226498
Offset: 1

Views

Author

Rick L. Shepherd, Oct 31 2009, Nov 01 2009

Keywords

Comments

Use definition 2 of vampire numbers; i.e., this is a subsequence of A014575.

Examples

			The vampire number 102510 is included because all of its digits, including the duplicate 0 and 1, can be rearranged to give at least one other vampire number such as 105210.

Crossrefs

Cf. A014575.

Extensions

Extended by Ray Chandler, Apr 26 2010
Previous Showing 11-17 of 17 results.

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