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 A248004 Least positive integer m with prime(m*n) == 1 (mod m+n). 9
 3, 4, 1, 2, 2, 15, 1, 1, 5, 10, 2, 3, 4, 18, 6, 27, 4, 7, 35, 4, 45, 2, 47, 9, 5, 10, 16, 11, 3, 3, 9, 61, 1, 52, 3, 60, 53, 74, 8, 47, 7, 60, 128, 5, 21, 12, 2, 29, 15, 127, 53, 28, 17, 21, 303, 80, 72, 8, 61, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: (i) a(n) exists for any n > 0. Moreover, a(n) does not exceed n*(n-1)/2 if n > 2. (ii) For each positive integer n, there is an integer m > 0 with prime(m*n) == -1 (mod m+n). Moreover, we may require that m does not exceed n*(n-1)/2 if n > 2. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014. EXAMPLE a(2) = 4 since prime(2*4) = 19 is congruent to 1 modulo 2 + 4 = 6. a(5146) = 593626 since prime(5146*593626) = prime(3054799396) = 73226821741 is congruent to 1 modulo 5146 + 593626 = 598772. MATHEMATICA Do[m=1; Label[aa]; If[Mod[Prime[m*n], m+n]==1, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}] lpim[n_]:=Module[{m=1}, While[Mod[Prime[m*n], m+n]!=1, m++]; m]; Array[lpim, 60] (* Harvey P. Dale, Oct 01 2017 *) CROSSREFS Cf. A000040, A247824, A247975. Sequence in context: A204999 A294731 A085710 * A106650 A076942 A205127 Adjacent sequences:  A248001 A248002 A248003 * A248005 A248006 A248007 KEYWORD nonn AUTHOR Zhi-Wei Sun, Sep 29 2014 STATUS approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)