A215641 -id:A215641 - cp's OEIS frontend

A340222 Constant whose decimal expansion is the concatenation of the largest n-digit semiprime A098450(n), for n = 1, 2, 3, ...

9, 9, 5, 9, 9, 8, 9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

M. F. Hasler, Jan 01 2021

			The smallest prime with 1, 2, 3, 4, ... digits is, respectively, 9 = 3^2, 95 = 5*19, 998 = 2*499, 9998 = 2*4999, .... Here we list the sequence of digits of these numbers: 9: 9, 5; 9, 9, 8; 9, 9, 9, 8; ...
This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.9959989998...

Cf. A098450 (largest n-digit semiprime), A340221 (similar, with smallest semiprime, limit of A215647), A340207 (same for squares, limit of A339978), A340206 (similar, with smallest n-digit squares, limit of A215689), A340209 (same with cubes, limit of A340115), A340208 (similar, with smallest n-digit cubes, limit of A215692), A340220 (same for primes, limit of A338968), A340219 (similar for smallest n-digit primes, limit of A215641).

Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).

concat([digits(A098450(k))|k<-[1..14]]) \\ as seq. of digits
c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*A098450(k)) \\ as constant

c = 0.995998999899998999997999999899999997999999991999999999799999999997...
  = Sum_{k >= 1} 10^(-k(k+1)/2)*A098450(k)
a(-n(n+1)/2) = 9 for all n >= 0, followed by increasingly more 9s.

A215685 Smallest prime whose decimal expansion consists of the concatenation of a 2-digit emirp, a 3-digit emirp, a 4-digit emirp, ..., and an n-digit emirp (A006567).

Original entry on oeis.org

13, 13337, 131071021, 13107100910711, 13107100910007100483, 131071009100071000491000187, 13107100910007100049100003310000657, 13107100910007100049100003310000169100007543, 131071009100071000491000033100001691000000071000015351

Offset: 2

Jonathan Vos Post, Aug 20 2012

If a(n) exists it has A000217(n)-1 digits.

			a(2) = 13 which is a prime, and whose decimal digits reversed, 31, is also a prime.
a(3) = 13337, which is a prime, and the concatenation of 13 (an emirp) and 337 (an emirp because 733 is also a prime). It happens that the digital reversal of a(3), 73331, is also prime, so that 13337 is an emirp, but that is not a requirement for this sequence.
Note that a(4) is a prime but not an emirp, because 12070131 = 3 * 61 * 65957.

Cf. A000040, A006567, A215641, A215647.

More terms from Alois P. Heinz, Aug 22 2012

cp's OEIS Frontend

A340222 Constant whose decimal expansion is the concatenation of the largest n-digit semiprime A098450(n), for n = 1, 2, 3, ...

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula