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 A078502 a(n) = smallest positive integer N such that (N - k)/k is prime for k = 1, 2, ..., n. 2
 3, 6, 12, 12, 174600, 7224840, 10780560, 10780560, 1086338816640, 50060257410240, 7720634052774720, 227457297898150320, 7272877497848202240, 7272877497848202240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The idea for the sequence and first eleven terms are from Ken Wilke. a(n) == 0 (mod 120) for n > 4: because a(n)/2, a(n)/3, a(n)/4 and a(n)/5 must be integer, a(n) == 0 (mod 60); and if a(n) == 60 (mod 120), (a(n)-4)/4 == 14 (mod 120) would not be prime; thus a(n) == 0 (mod 120). A more general result is a(n) == 0 (mod lcm(1,2,...,n)) for all n >= 1, and a(n) == 0 (mod 2*lcm(1,2,...,n)) for n > 4. - Jean-Christophe Hervé, Sep 15 2014 LINKS Table of n, a(n) for n=1..14. Carlos Rivera, Puzzle 206. (N-k)/k Primes, Prime Puzzles and Problems Connection. Carlos Rivera, Puzzle 977. A special set of primes, Prime Puzzles and Problems Connection. G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 7272877497848202240 FORMULA a(n) == 0 (mod A003418(n)) because of the divisibility condition (A003418(n) = lcm(1,2,...,n)). - Jean-Christophe Hervé, Sep 15 2014 EXAMPLE (12-k)/k is prime for k = 1,2,3,4 and 12 is the smallest positive integer satisfying this property. Hence a(4) = 12. PROG (PARI) a(n)=k=1; while(k, c=0; for(i=1, n, if(k%i==0&&isprime(k/i-1), c++)); if(c==n, return(k)); k++) n=1; while(n<10, print1(a(n), ", "); n++) \\ Derek Orr, Sep 15 2014 CROSSREFS See A093554 for another version. Cf. A074200 (equivalent sequence for (N+k)/k prime). Sequence in context: A182633 A038587 A090553 * A107974 A298879 A116625 Adjacent sequences: A078499 A078500 A078501 * A078503 A078504 A078505 KEYWORD nonn,more AUTHOR Joseph L. Pe, Jan 05 2003 EXTENSIONS Corrected and extended by Jens Kruse Andersen, Jan 10 2003 STATUS approved

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Last modified December 7 18:28 EST 2023. Contains 367660 sequences. (Running on oeis4.)