

A269233


a(n) = number of "candidate primes" < A037053(n). (See Comments for description and explanation.)


2



0, 0, 3, 2, 1, 1, 5, 2, 2, 8, 1, 5, 12, 46, 20, 5, 1, 1, 22, 17, 31, 3, 51, 2, 7, 20, 32, 8, 10, 45, 17, 56, 93, 59, 5, 8, 31, 20, 1, 13, 57, 17, 44, 80, 3, 27, 88, 59, 3, 92, 198, 34, 34, 40
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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[nk zeros]a[k zeros]b {k=1..n}, then {2..9}[nk 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


LINKS

Table of n, a(n) for n=0..53.


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

Cf. A037053, A270095 (records).
Sequence in context: A329231 A259341 A046225 * A123396 A225800 A176669
Adjacent sequences: A269230 A269231 A269232 * A269234 A269235 A269236


KEYWORD

nonn,base


AUTHOR

Bob Selcoe, Feb 20 2016


EXTENSIONS

Corrected a(15) & fixed Example typo.  Hans Havermann, Feb 21 2016


STATUS

approved



