login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A037055 Smallest prime containing exactly n 1's. 16
2, 13, 11, 1117, 10111, 101111, 1111151, 11110111, 101111111, 1111111121, 11111111113, 101111111111, 1111111118111, 11111111111411, 111111111116111, 1111111111111181, 11111111101111111, 101111111111111111, 1111111111111111171, 1111111111111111111, 111111111111111119111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n > 1, A037055 is conjectured to be identical to A084673. - Robert G. Wilson v, Jul 04 2003

a(n) =  A002275(n) for n in A004023.  For all other n < 900, a(n) has n+1 digits. - Robert Israel, Feb 21 2016

LINKS

Robert Israel, Table of n, a(n) for n = 0..900

FORMULA

a(n) = the smallest prime in { R-10^n, R-10^(n-1), ..., R-10; R+a*10^b, a=1, ..., 8, b=0, 1, 2, ..., n }, where R = (10^(n+1)-1)/9 is the (n+1)-digit repunit. - M. F. Hasler, Feb 25 2016

MAPLE

f:= proc(n) local m, d, r, x;

   r:= (10^n-1)/9;

   if isprime(r) then return r fi;

   r:= (10^(n+1)-1)/9;

   for m from n-1 to 1 by -1 do

     x:= r - 10^m;

     if isprime(x) then return x fi;

   od;

   for m from 0 to n do

     for d from 1 to 8 do

        x:= r + d*10^m;

        if isprime(x) then return x fi;

     od

   od;

   error("Needs more than n+1 digits")

end proc:

map(f, [$0..100]); # Robert Israel, Feb 21 2016

MATHEMATICA

f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[b, {i, 1, n}], {x}]], c = Complement[Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[r ? Infinity, r, p = Permutations[ Join[ Table[ b, {i, 1, n}], {x, y}]]; q = {}; Do[q = Append[q, Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]]]; Table[ f[n, 1], {n, 1, 18}]

PROG

(PARI) A037055(n)={my(p, t=10^(n+1)\9); forstep(k=n+1, 1, -1, ispseudoprime(p=t-10^k) && return(p)); forvec(v=[[0, n], [1, 8]], ispseudoprime(p=t+10^v[1]*v[2]) && return(p))} \\ M. F. Hasler, Feb 22 2016

CROSSREFS

Cf. A084673, A065584, A065821, A037054, A034388, A036507-A036536.

Cf. A037053, A037057, A037059, A037061, A037063, A037065, A037067, A037069, A037071.

Sequence in context: A213306 A213307 A213305 * A065584 A153651 A229908

Adjacent sequences:  A037052 A037053 A037054 * A037056 A037057 A037058

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Jan 04 1999

EXTENSIONS

More terms from Sascha Kurz, Feb 10 2003

Edited by Robert G. Wilson v, Jul 04 2003

a(0) = 2 inserted by Robert Israel, Feb 21 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 28 21:44 EDT 2016. Contains 275935 sequences.