A269233 a(n) = number of "candidate primes" < A037053(n). (See Comments for description and explanation.)

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

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

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: A350733 A351073 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