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 11 results. Next

A317920 Length of row n of A317721, i.e., number of elements in n-th Wieferich tuple when ordering the tuples as in A317721.

Original entry on oeis.org

3, 5, 6, 7, 6, 7, 3, 8, 9, 9, 10, 10, 11, 9, 2, 3, 6, 9, 10, 11, 12, 13, 14, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12
Offset: 1

Views

Author

Felix Fröhlich, Aug 21 2018

Keywords

Examples

			For n = 1: Row 1 of A317721 has 3 elements, i.e., the first Wieferich tuple listed in A317721 is a "Wieferich triple", so a(1) = 3.

Crossrefs

Cf. A297846, A317721, A317919.

Programs

  • PARI
    addtovec(vec) = my(w=[], vmax=0); for(t=1, #vec, if(vecmax(vec[t]) > vmax, vmax=vecmax(vec[t]))); for(k=1, #vec, forprime(q=1, vmax, if(Mod(vec[k][#vec[k]], q^2)^(q-1)==1, w=concat(w, [0]); w[#w]=concat(vec[k], [q])))); w
removefromvec(vec) = my(w=[]); for(k=1, #vec, if(vecsort(vec[k])==vecsort(vec[k], , 8), w=concat(w, [0]); w[#w]=vec[k])); w
printfromvec(vec) = for(k=1, #vec, if(vec[k][1]==vec[k][#vec[k]], print1(#vec[k]-1, ", ")))
forprime(p=1, , my(v=[[p]]); while(#v > 0, v=addtovec(v); printfromvec(v); v=removefromvec(v)))

A317919 Number of Wieferich tuples with A297846(n) as largest member, i.e., number of rows of the array in A317721 where A297846(n) is the largest element of that row.

Original entry on oeis.org

1, 3, 2, 7, 1, 2, 1, 6, 1, 317, 1, 1, 230, 580
Offset: 1

Views

Author

Felix Fröhlich, Aug 21 2018

Keywords

Examples

			For n = 2: The second prime that occurs in column 1 of the array in A317721 is 359. 359 occurs as the largest element in 3 rows of the array, so a(2) = 3.

Crossrefs

Cf. A297846, A317721, A317920.

Programs

  • PARI
    addtovec(vec) = my(w=[], vmax=0); for(t=1, #vec, if(vecmax(vec[t]) > vmax, vmax=vecmax(vec[t]))); for(k=1, #vec, forprime(q=1, vmax, if(Mod(vec[k][#vec[k]], q^2)^(q-1)==1, w=concat(w, [0]); w[#w]=concat(vec[k], [q])))); w
removefromvec(vec) = my(w=[]); for(k=1, #vec, if(vecsort(vec[k])==vecsort(vec[k], , 8), w=concat(w, [0]); w[#w]=vec[k])); w
forprime(p=1, , my(v=[[p]], i=0); while(#v > 0, v=addtovec(v); for(k=1, #v, if(v[k][1]==v[k][#v[k]], i++)); v=removefromvec(v)); if(i > 0, print1(i, ", ")))

A344282 Column 1 of A317721.

Original entry on oeis.org

71, 359, 359, 359, 487, 487, 863, 863, 863, 863, 863, 863, 863, 1069, 1093, 1093, 1483, 1549, 1549, 1549, 1549, 1549, 1549, 2281, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511, 3511
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Comments

A297846 with each term repeated A317919(n) times.

Crossrefs

Cf. A297846, A317721, A317919, A344283 (column 2).

Programs

  • PARI
    addtovec(vec) = my(w=[], vmax=0); for(t=1, #vec, if(vecmax(vec[t]) > vmax, vmax=vecmax(vec[t]))); for(k=1, #vec, forprime(q=1, vmax, if(Mod(vec[k][#vec[k]], q^2)^(q-1)==1, w=concat(w, [0]); w[#w]=concat(vec[k], [q])))); w
removefromvec(vec) = my(w=[]); for(k=1, #vec, if(vecsort(vec[k])==vecsort(vec[k], , 8), w=concat(w, [0]); w[#w]=vec[k])); w
printfromvec(vec) = for(k=1, #vec, if(vec[k][1]==vec[k][#vec[k]], print1(vec[k][1], ", ")))
forprime(p=1, , my(v=[[p]]); while(#v > 0, v=addtovec(v); printfromvec(v); v=removefromvec(v)))

A344283 Column 2 of A317721.

Original entry on oeis.org

3, 3, 307, 307, 11, 3, 23, 3, 3, 467, 3, 467, 467, 37, 2, 5, 31, 3, 127, 127, 127, 127, 127, 1667, 73, 19, 19, 19, 19, 19, 31, 31, 19, 31, 19, 19, 31, 31, 31, 31, 31, 31, 19, 31, 3, 3, 31, 31, 3, 3, 3, 3, 19, 19, 31, 31, 73, 73, 3, 3, 3, 3, 3, 3, 3, 19, 19, 31
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Cf. A317721, A344282 (column 1).

Programs

  • PARI
    addtovec(vec) = my(w=[], vmax=0); for(t=1, #vec, if(vecmax(vec[t]) > vmax, vmax=vecmax(vec[t]))); for(k=1, #vec, forprime(q=1, vmax, if(Mod(vec[k][#vec[k]], q^2)^(q-1)==1, w=concat(w, [0]); w[#w]=concat(vec[k], [q])))); w
removefromvec(vec) = my(w=[]); for(k=1, #vec, if(vecsort(vec[k])==vecsort(vec[k], , 8), w=concat(w, [0]); w[#w]=vec[k])); w
printfromvec(vec) = for(k=1, #vec, if(vec[k][1]==vec[k][#vec[k]], print1(vec[k][2], ", ")))
forprime(p=1, , my(v=[[p]]); while(#v > 0, v=addtovec(v); printfromvec(v); v=removefromvec(v)))

A307639 Irregular array T(n, k) read by rows, where row n lists the members of n-th Fermat pseudoprime tuple. Rows are arranged first by size of largest term, then by increasing length of row, then in lexicographic order.

Original entry on oeis.org

9, 8, 15, 14, 21, 20, 21, 10, 9, 8, 25, 24, 27, 26, 28, 9, 28, 27, 26, 9, 28, 27, 26, 25, 28, 27, 26, 25, 8, 9, 28, 27, 26, 25, 8, 21, 10, 9, 33, 32, 33, 8, 21, 10, 33, 32, 25, 8, 21, 10, 33, 32, 25, 28, 9, 8, 21, 10, 33, 32, 25, 28, 27, 26, 9, 8, 21, 10
Offset: 1

Views

Author

Felix Fröhlich, Apr 19 2019

Keywords

Comments

Let c_1, c_2, c_3, ..., c_u be a set C of distinct composites and let m_1, m_2, m_3, ..., m_u be a set V of variables. Then C is a Fermat pseudoprime u-tuple if there exists a mapping from the elements of C to the elements of V such that each of the following congruences is satisfied: m_1^(m_2-1) == 1 (mod m_2), m_2^(m_3-1) == 1 (mod m_3), ..., m_u^(m_1-1) == 1 (mod m_1).

Examples

			Irregular array starts as follows:
   9,  8
  15, 14
  21, 20
  21, 10, 9, 8
  25, 24
  27, 26
  28,  9
  28, 27, 26,  9
  28, 27, 26, 25
  28, 27, 26, 25, 8,  9
  28, 27, 26, 25, 8, 21, 10, 9
  33, 32
  33,  8, 21, 10
  33, 32, 25,  8, 21, 10
  33, 32, 25, 28,  9,  8, 21, 10
  33, 32, 25, 28, 27, 26,  9,  8, 21, 10
  35, 34
  35, 34, 33, 32, 25,  6
  35,  9, 28, 27, 26, 25,  6
  35, 34, 21, 10, 33, 32, 25,  6
  35,  9,  8, 21, 10, 33, 32, 25,  6
  35, 34, 21, 10,  9, 28, 27, 26, 25,  6
  35, 34, 33,  8,  9, 28, 27, 26, 25,  6
  35, 34, 21, 10, 33,  8,  9, 28, 27, 26, 25,  6
  35, 34, 33,  8, 21, 10,  9, 28, 27, 26, 25,  6
  39, 38
The composites 21, 10, 9 and 8 satisfy the congruences 21^(10-1) == 1 (mod 10), 10^(9-1) == 1 (mod 9), 9^(8-1) == 1 (mod 8) and 8^(21-1) == 1 (mod 21), so 21, 10, 9, 8 is a row of the array.

Crossrefs

Cf. A317721.

Programs

  • PARI
    addtovec(vec) = my(w=[], vmax=0); for(t=1, #vec, if(vecmax(vec[t]) > vmax, vmax=vecmax(vec[t]))); for(k=1, #vec, forcomposite(c=1, vmax, if(Mod(vec[k][#vec[k]], c)^(c-1)==1, w=concat(w, [0]); w[#w]=concat(vec[k], [c])))); w
removefromvec(vec) = my(w=[]); for(k=1, #vec, if(vecsort(vec[k])==vecsort(vec[k], , 8), w=concat(w, [0]); w[#w]=vec[k])); w
printfromvec(vec) = for(k=1, #vec, if(vec[k][1]==vec[k][#vec[k]], for(t=1, #vec[k]-1, print1(vec[k][t], ", ")); print("")))
forcomposite(c=1, 40, my(v=[[c]]); while(#v > 0, v=addtovec(v); printfromvec(v); v=removefromvec(v)))

A344284 Primes that are the largest member of a Wieferich 5-tuple.

Original entry on oeis.org

359, 3511, 6451, 6733
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Subsequence of A297846. Cf. A317721, A317920.

A344285 Primes that are the largest member of a Wieferich 6-tuple.

Original entry on oeis.org

359, 487, 1483, 3511
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Subsequence of A297846. Cf. A317721, A317920.

A344286 Primes that are the largest member of a Wieferich 7-tuple.

Original entry on oeis.org

359, 487, 3511
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Subsequence of A297846. Cf. A317721, A317920.

A344287 Primes that are the largest member of a Wieferich 8-tuple.

Original entry on oeis.org

863, 3511, 6733, 7393
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Subsequence of A297846. Cf. A317721, A317920.

A344288 Primes that are the largest member of a Wieferich 9-tuple.

Original entry on oeis.org

863, 1069, 1549, 3511
Offset: 1

Views

Author

Felix Fröhlich, May 14 2021

Keywords

Crossrefs

Subsequence of A297846. Cf. A317721, A317920.
Showing 1-10 of 11 results. Next

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