A123216 - OEIS

%I #16 Jul 05 2024 08:12:26

%S 2,37,677,10061,132241,1632899,19394489,224284387,2543568463,

%T 313945524931,37301821050191,4317408693770701,490210240132738471

%N Concatenated index primes. Primes whose indices are the concatenation of the consecutive integers.

%C a(10) was taken from a file of all primes < 1 trillion. The next term, prime(1234567891011) ~ 37301821238347 is exact in the first 7 places. This and larger indices can be computed with an exponential bisection routine given in the link.

%H Cino Hilliard, <a href="https://web.archive.org/web/20080606013645/http://groups.msn.com/NthprimeAlgorithms/nthprimeapproximation.msnw">Approximation for the Nth prime</a>.

%F a(n) = prime(A007908(n)). - _Amiram Eldar_, Jul 05 2024

%e The concatenation of the first three integers is 123. Prime(123) = 677, the 3rd term.

%t Prime@*FromDigits@*Flatten@*IntegerDigits@*Range~Array~10 (* _Giorgos Kalogeropoulos_, Oct 19 2022 *)

%o (PARI) g(n) = st="";for(x=1,n,st=concat(st,Str(x));print1(prime(eval(st))","))

%Y Cf. A007908.

%K nonn,base,more

%O 1,1

%A _Cino Hilliard_, Oct 06 2006

%E a(11) from _Giorgos Kalogeropoulos_, Oct 19 2022

%E a(12)-a(13) from _Amiram Eldar_, Jul 05 2024