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.

User: Per H. Lundow

Per H. Lundow's wiki page.

Per H. Lundow has authored 75 sequences. Here are the ten most recent ones:

A185122 a(n) = minimum pandigital prime in base n.

Original entry on oeis.org

2, 11, 283, 3319, 48761, 863231, 17119607, 393474749, 10123457689, 290522736467, 8989787252711, 304978405943587, 11177758345241723, 442074237951168419, 18528729602926047181, 830471669159330267737, 39482554816041508293677, 1990006276023222816118943, 105148064265927977839670339, 5857193485931947477684595711
Offset: 2

Author

Per H. Lundow, Jan 16 2012

Keywords

Comments

a(n) is the smallest prime whose base-n representation contains all digits (i.e., 0,1,...,n-1) at least once.

Examples

			The corresponding base-b representations are:
2  10
3  102
4  10123
5  101234
6  1013425
7  10223465
8  101234567
9  1012346785
10 10123457689
11 1022345689a7
12 101234568a79b
13 10123456789abc
14 10123456789cdab
15 10223456789adbce
...
		

Programs

  • Python
    from math import gcd
    from itertools import count
    from sympy import nextprime
    from sympy.ntheory import digits
    def A185122(n):
        m = n
        j = 0
        if n > 3:
            for j in range(1,n):
                if gcd((n*(n-1)>>1)+j,n-1) == 1:
                     break
        if j == 0:
            for i in range(2,n):
                m = n*m+i
        elif j == 1:
            for i in range(1,n):
                m = n*m+i
        else:
            for i in range(2,1+j):
                m = n*m+i
            for i in range(j,n):
                m = n*m+i
        m -= 1
        while True:
            if len(set(digits(m:=nextprime(m),n)[1:]))==n:
                return m # Chai Wah Wu, Mar 12 2024

A028449 Number of perfect matchings in graph P_{2} X P_{5} X P_{n}.

Original entry on oeis.org

1, 8, 450, 14320, 535229, 19114420, 692276437, 24972353440, 901990734650, 32567565264292, 1176040842289105, 42466317504553328, 1533458728878759825, 55373015618048484484, 1999515562849410856778, 72202339448101503740768, 2607220750517054436937621
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Crossrefs

Column k=5 of A181206.

Formula

G.f.: see link above.

A033526 Number of matchings in graph P_{2} X P_{3} X P_{n}.

Original entry on oeis.org

1, 22, 1511, 90040, 5493583, 334056618, 20324827981, 1236501116120, 75226160041933, 4576591071807054, 278429681683117411, 16939044773645481920, 1030533959174319758227, 62695402974582513118434, 3814249420035058238741393, 232050484511869215926762256
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

Formula

G.f.: (-x^22 +2*x^21 +105*x^20 -408*x^19 -2333*x^18 +11980*x^17 +12081*x^16 -112640*x^15 +25122*x^14 +435060*x^13 -292630*x^12 -741024*x^11 +647902*x^10 +512680*x^9 -535258*x^8 -85184*x^7 +168951*x^6 -24902*x^5 -12107*x^4 +3384*x^3 -57*x^2 -36*x +1) / (x^24 -4*x^23 -148*x^22 +636*x^21 +5486*x^20 -25774*x^19 -66616*x^18 +377290*x^17 +207927*x^16 -2210908*x^15 +370396*x^14 +5950068*x^13 -2989756*x^12 -7411696*x^11 +5362636*x^10 +3624000*x^9 -3734313*x^8 -139824*x^7 +897064*x^6 -240512*x^5 -5090*x^4 +7406*x^3 -292*x^2 -58*x +1). - Alois P. Heinz, Dec 09 2013

A033527 Number of matchings in graph P_{2} X P_{4} X P_{n}.

Original entry on oeis.org

1, 71, 21497, 5493583, 1441534384, 376940962215, 98618371821449, 25799240154157639, 6749345823947488233, 1765694380951147363456, 461922949276035424430681, 120843562204869252316712655, 31613858308925485200467329841, 8270494656919429771594190182151
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033528 Number of matchings in graph P_{2} X P_{5} X P_{n}.

Original entry on oeis.org

1, 228, 305184, 334056618, 376940962215, 423657524608288, 476450515130518749, 535774070372040050788, 602492787376187496898304, 677518242019979197787376936, 761886547661136372157201911987, 856760801962209647160995669509984, 963449325363457811035756544808212891
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033529 Number of matchings in graph P_{2} X P_{6} X P_{n}.

Original entry on oeis.org

1, 733, 4334009, 20324827981, 98618371821449, 476450515130518749, 2303329608950881340608, 11134067093100203643948181, 53821768256990554940684650505, 260172308883754886843036887611589, 1257663186848063684537091601425009561
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033530 Number of matchings in graph P_{3} X P_{3} X P_{n}.

Original entry on oeis.org

1, 131, 90040, 49793133, 28579431833, 16294017491392, 9303034425177393, 5309783310438438755, 3030852157018381983096, 1729989715204411185894125, 987471788038820650012763705, 563644449821238971691233574464, 321725839534452657823357410831785
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033531 Number of matchings in graph P_{3} X P_{4} X P_{n}.

Original entry on oeis.org

1, 823, 5493583, 28579431833, 154620656140976, 831415352314053207, 4475746196648151844135, 24088698990102061728597981, 129653063594088631745065442153, 697826352881007761016861345617984, 3755891812799886342646421870514820641
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033533 Number of matchings in graph P_{4} X P_{4} X P_{n}.

Original entry on oeis.org

1, 10012, 1441534384, 154620656140976, 17312701462385916505, 1926836037115087006553088, 214664979834173287380956088153, 23911146651705731250582573707211200
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

A033534 Number of matchings in graph P_{5} X P_{5} X P_{n}.

Original entry on oeis.org

1, 2810694, 423657524608288, 42127221925485860896792, 4435122353330774501960785797973, 463310369790129032480118384076035223552
Offset: 0

Author

Keywords

References

  • Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.