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.

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

1,1

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).

Links

Table of n, a(n) for n=1..68.

Example

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.

Prog

(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)))

Crossrefs

Cf. A317721.

Sequence in context: A004450 A272962 A137392 * A231483 A309656 A370882

Adjacent sequences: A307636 A307637 A307638 * A307640 A307641 A307642

Keyword

nonn,tabf

Author

Felix Fröhlich, Apr 19 2019

Status

approved