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A258433 Primes with repdigit indices (in decimal). 2


%S 2,3,5,7,11,13,17,19,23,31,79,137,193,257,317,389,457,523,607,1399,

%T 2239,3119,4019,4973,5903,6907,7907,8933,19583,30911,42473,54581,

%U 66889,79357,92003,104723,117763,252233,393191,538259,686671,836833,989999,1144153,1299689,1456667,3080969,4767181,6495109,8251153

%N Primes with repdigit indices (in decimal).

%C Elements of this sequence are the first 9 primes, then the 11th, 22nd, 33rd, ... , 99th, 111th, 222nd, etc. This is a somewhat remarkable sequence because of certain digital coincidences (see Prime Curios links).

%H Charles R Greathouse IV, <a href="/A258433/b258433.txt">Table of n, a(n) for n = 1..153</a>

%H Andrew Booker, <a href="http://primes.utm.edu/nthprime/index.php#nth">The Nth Prime Page</a>

%H Prime Curios!, <a href="http://primes.utm.edu/curios/page.php/989999.html">989999</a>

%H Prime Curios!, <a href="http://primes.utm.edu/curios/page.php?number_id=13076">640663963</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Repdigit">Repdigit</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime-counting_function">Prime-counting function</a>

%F a(n) = A000040(A010785(n)).

%e The first prime skipped is the 10th, 29, so that a(10)=31. Then follows a(11)=79, a(12)=137, a(13)=193, etc.: The 22nd, 33rd, and 44th primes, and so on.

%t Prime[#]&/@(FromDigits/@Flatten[Table[PadRight[{},k,n],{k,6},{n,9}],1]) (* _Harvey P. Dale_, Mar 25 2019 *)

%o (PARI) a(n)=prime(10^((n+8)\9)\9*((n-1)%9+1)) \\ _Charles R Greathouse IV_, Jun 03 2015

%Y Cf. A000040, A010785, A105581.

%K nonn,base

%O 1,1

%A _James G. Merickel_, May 29 2015

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)