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 A078728 a(n) is the smallest m such that m < 10^n, 10^n + m is prime and if the natural number k is such that 1 < k < 10 and 3 doesn't divide k*10^n + m then k*10^n+m is prime. 0
 3, 57, 297, 177, 237, 25111, 231339, 67419, 273817, 345111, 2001753, 912277, 5236153, 9228627, 10599391, 2835261, 60120003, 14054037, 27923629, 41783347, 24590943, 112161513, 230484021, 11446969, 205242589, 583389307, 873650007 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the smallest m such that m < 10^n and all six numbers 10^n + m, (Mod[m, 3]+2)*10^n + m, 4*10^n + m, (Mod[m, 3]+5)*10^n + m, 7*10^n + m & (Mod[m, 3]+8)*10^n + m are primes. Carlos Rivera in Puzzle 245 of www.primepuzzles.net wrote "if the Faride's results ( a(n) for n=1,...,24 ) are plotted in Excel and a trend 'potential' function is asked, we obtain that a(n) is approximately equal to 0.5*n^6; this means that for n=999 a(n)=5*10^17, approximately." Since 10^n+a(n) is prime, for each n a(n)=0 (mod 3) or a(n)=1 (mod 3). LINKS Table of n, a(n) for n=1..27. Carlos Rivera, Puzzle 245. As 13 FORMULA a[n_] := (For[m=1, !PrimeQ[10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+2)10^n+2m-1]||! PrimeQ[4*10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+5)10^n+2m-1]||!PrimeQ [7*10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+8)10^n+2m-1], m++ ];2m-1) EXAMPLE a(6)=25111 because all the six numbers 1025111, 3025111, 4025111, 6025111, 7025111, 9025111 are primes and 25111 is the smallest number with this property. MATHEMATICA a[n_] := (For[m=1, !PrimeQ[10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+2)10^n+2m-1]||! PrimeQ[4*10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+5)10^n+2m-1]||!PrimeQ [7*10^n+2m-1]||!PrimeQ[(Mod[2m-1, 3]+8)10^n+2m-1], m++ ]; 2m-1); Do[Print[a[n]], {n, 32}] CROSSREFS Cf. A003617, A033873. Cf. A091199. Sequence in context: A203483 A051227 A122548 * A032696 A337790 A131466 Adjacent sequences: A078725 A078726 A078727 * A078729 A078730 A078731 KEYWORD nonn AUTHOR Farideh Firoozbakht, Dec 26 2003 STATUS approved

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Last modified October 2 02:58 EDT 2023. Contains 365831 sequences. (Running on oeis4.)