A123216 Concatenated index primes. Primes whose indices are the concatenation of the consecutive integers.

2, 37, 677, 10061, 132241, 1632899, 19394489, 224284387, 2543568463, 313945524931, 37301821050191

Offset

1,1

Comments

The last term 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.

Links

Table of n, a(n) for n=1..11.

Cino Hilliard, Approximation for the Nth prime.

Example

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

Mathematica

Prime@*FromDigits@*Flatten@*IntegerDigits@*Range~Array~10 (* Giorgos Kalogeropoulos, Oct 19 2022 *)

Prog

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

Crossrefs

Sequence in context: A337306 A216539 A139122 * A307318 A058245 A257995

Adjacent sequences: A123213 A123214 A123215 * A123217 A123218 A123219

Keyword

more,nonn,base

Author

Cino Hilliard, Oct 06 2006

Extensions

a(11) from Giorgos Kalogeropoulos, Oct 19 2022

Status

approved