OFFSET
0,3
COMMENTS
A037053(n) = the smallest prime containing exactly n zeros. After A037053(0)=2, the smallest possible terms ("candidate primes") in A037053 are of the form a[n zeros]b, a in {1..9}, b in {1,3,7,9}; the first such being 1[n zeros]1. These are followed by forms 1[n zeros]ab, 1[n-k zeros]a[k zeros]b {k=1..n}, then {2..9}[n-k zeros]a[k zeros]b, etc. The present sequence represents the number of smaller candidates which are excluded before a prime occurs. See Examples below and A037053 for additional details.
These numbers will never appear: 12k+4, 12k+6, 12k+9, 12k+11, for k = 0 to 2, and 12k, 12k+2, 12k+5, 12k+7, for k > 2. - Hans Havermann, Feb 23 2016
Additionally, 26 will never appear. - Hans Havermann, Mar 10 2016
EXAMPLE
a(1)=0 because the smallest possible (candidate) prime containing one zero is 101, which is prime.
a(6)=5 because A037053(6)=20000003; the five smaller candidates {10000001, 10000003, 10000007, 10000009, 20000001} are composite.
a(13)=46 because A037053(13)=1000000000000037; the 36 smaller candidates of the form {1..9}[13 zeros]{1,3,7,9} are composite, as are the 10 candidates 1[13 zeros]{1,2}{1,3,7,9} and 1[13 zeros]3{1,3}.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bob Selcoe, Feb 20 2016
EXTENSIONS
Corrected a(15) & fixed Example typo. - Hans Havermann, Feb 21 2016
STATUS
approved