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 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}] Join[{2, 13}, Table[Sort[Flatten[Table[Select[FromDigits/@Permutations[Join[{n}, PadRight[{}, i, 1]]], PrimeQ], {n, 0, 9}]]][[1]], {i, 2, 20}]] (* Vincenzo Librandi, May 11 2017 *) 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: A213307 A213305 A002591 * 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

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)