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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 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 FrÃ¶hlich, Apr 19 2019 STATUS approved

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