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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A309657

Adjacent sequences:  A307636 A307637 A307638 * A307640 A307641 A307642

KEYWORD

nonn,tabf

AUTHOR

Felix Fröhlich, Apr 19 2019

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)