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A123216
Concatenated index primes. Primes whose indices are the concatenation of the consecutive integers.
0
2, 37, 677, 10061, 132241, 1632899, 19394489, 224284387, 2543568463, 313945524931, 37301821050191, 4317408693770701, 490210240132738471
OFFSET
1,1
COMMENTS
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.
FORMULA
a(n) = prime(A007908(n)). - Amiram Eldar, Jul 05 2024
EXAMPLE
The concatenation of the first three integers is 123. Prime(123) = 677, the 3rd term.
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
Cf. A007908.
Sequence in context: A337306 A216539 A139122 * A307318 A058245 A257995
KEYWORD
nonn,base,more
AUTHOR
Cino Hilliard, Oct 06 2006
EXTENSIONS
a(11) from Giorgos Kalogeropoulos, Oct 19 2022
a(12)-a(13) from Amiram Eldar, Jul 05 2024
STATUS
approved