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 A280017 Numbers k such that (10^k - 13)/3 is prime. 0
 2, 4, 5, 8, 11, 25, 35, 270, 401, 613, 635, 768, 1283, 2941, 3409, 4266, 4391, 10744, 22979, 26766, 27743, 35514, 59174, 86906, 99239, 154494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For k > 1, numbers such that k - 2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section). a(27) > 2 * 10^5. - Price There are no odd multiples of 3 in this sequence. If k is an odd multiple of 3, then (10^k - 13)/3 is divisible by 7. The smallest even multiple of 3 in the sequence is 270. - Alonso del Arte, Dec 31 2017 LINKS Makoto Kamada, Factorization of near-repdigit-related numbers. Makoto Kamada, Search for 3w29. EXAMPLE 4 is in this sequence because (10^4 - 13)/3 = 3329 is prime. Here is a listing of the initial terms and associated primes: a(1) = 2, 29; a(2) = 4, 3329; a(3) = 5, 33329; a(4) = 8, 33333329; a(5) = 11, 33333333329; etc. MATHEMATICA Select[Range[2, 100000], PrimeQ[(10^# - 13)/3] &] PROG (PARI) isok(n) = isprime((10^n-13)/3); \\ Altug Alkan, Dec 31 2017 CROSSREFS Cf. A056707 (numerators of (10^k - 13)/3 that are prime for k negative), A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269. Sequence in context: A288523 A240179 A295032 * A080136 A080033 A007379 Adjacent sequences:  A280014 A280015 A280016 * A280018 A280019 A280020 KEYWORD nonn,more,hard,changed AUTHOR Robert Price, Feb 21 2017 EXTENSIONS a(26) from Robert Price, Dec 31 2017 STATUS approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)