Ambiguity in sequence A073175 First occurrence of an n-digit prime as a substring in the concatenation of the natural numbers
Jonathan Post
jvospost3 at gmail.com
Wed Aug 27 21:03:31 CEST 2008
Another clarification to connect several existing and several impliedsequences is as follows.
Axxxxx1 = leftmost n digits of A019518 Smarandache-Wellin numbers:a(n) = concatenation of first n primes = first n digits of the decimal0.23571113171923... (A033308) = Copeland-Erdős constant.
n a(n)1 22 233 2354 23575 235716 2357117 23571118 235711139 23571113110 2357111317and so forth.
Axxxxx2 = leftmost n digits of Champernowne's constant0.12345678910111213... (A033307) cf. A007908
n a(n)1 12 123 1234 12345 123456 1234567 12345678 123456789 12345678910 123456789111 1234567891012 12345678910113 1234567891011an so forth.
We can now derive the sequences of the first occurrence of Axxxxx1 inAxxxxx2, and vice versa.
For example:
n a(n)1 1 1=A007908(1) a substring of 11=prime(5)2 127 12 =A007908(2) a substring of 127=prime(31)3 1231 123=A007908(3) a substring of 1231=prime(202)4 12347 1234=A07908(4) a substring of 12347=prime(1475)5 123457 12345 a substring of prime(11602)and so forth.
This approach fills gaps, allows symmetry, adds cross-references,connects with two interesting real constants (links to their pages inMathWorld), and eliminates ambiguities stemming from digit-countingand presence of zeros.
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