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A037053 Smallest prime containing exactly n 0's. +0
14
101, 1009, 10007, 100003, 1000003, 20000003, 100000007, 1000000007, 30000000001, 100000000003, 2000000000003, 40000000000001, 1000000000000037, 6000000000000001, 20000000000000003, 100000000000000003 (list; graph; listen)
OFFSET

1,1

COMMENT

Notice that certain entries require n+3 digits such as a(13). Those which do not require three digits besides n zeros are in A085824. Conjecture, a prime of this form, A037053, requires at most three judiciously placed digits, two on the exterior and one inside. - Robert G. Wilson v.

MATHEMATICA

a[n_List] := Join[{x}, n, {y}]; f[n_] := Block[{p = Join[{x}, Table[ 0, {i, 1, n}], {y}], c = Table[j, {j, 1, 9}], q = {}}, Do[q = Append[q, Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; r = Min[ Select[ FromDigits /@ q, PrimeQ[ # ] & ]]; If[r != Infinity, r, p = Permutations[ Join[ Table[0, {i, 1, n}], {d}]]; p = Map[a, p]; q = {}; Do[q = Append[q, Replace[p, {d -> c[[i]], x -> c[[j]], y -> c[[k]]}, 2]], {i, 1, 9}, {j, 1, 9}, {k, 1, 9}]; Min[ Select[

CROSSREFS

Cf. A037052, A034388, A085824, A036507-A036536.

Cf. A037055, A037057, A037059, A037061, A037063, A037065, A037067.

Sequence in context: A089291 A082276 A069597 this_sequence A139535 A139536 A115820

Adjacent sequences: A037050 A037051 A037052 this_sequence A037054 A037055 A037056

KEYWORD

nonn,base

AUTHOR

Patrick De Geest (pdg(AT)worldofnumbers.com), Jan 04 1999.

EXTENSIONS

More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Aug 16 2002

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2003

Jul 09 2003: Zakir Seidov comments that the Mma program is incorrect. The sequence should be recheked.

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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