A037067 Smallest prime containing exactly n 7's.
2, 7, 277, 1777, 47777, 727777, 7477777, 77767777, 577777777, 1777777777, 67777777777, 377777777777, 7177777777777, 17777777777777, 577777777777777, 2777777777777777, 77777767777777777, 377777777777777777, 2777777777777777777, 71777777777777777777
Offset: 0
Links
- M. F. Hasler and Robert Israel, Table of n, a(n) for n = 0..998 (n = 0..200 from M. F. Hasler)
Crossrefs
Programs
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Maple
F:= proc(n) local x0,i,j; x0:= 7/9*(10^(n+1)-1); for j from 1 to 6 do if isprime(x0 + (j-7)*10^n) then return x0 + (j-7)*10^n fi od; for i from n-1 to 0 by -1 do for j from 0 to 6 do if isprime(x0 + (j-7)*10^i) then return x0 + (j-7)*10^i fi od od; for i from 0 to n do for j from 8 to 9 do if isprime(x0 + (j-7)*10^i) then return x0 + (j-7)*10^i fi od od: end proc: F(0):= 2: F(1):= 7: map(F, [$0..100]); # Robert Israel, Jul 13 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, 7], {n, 1, 18}] -
PARI
A037067(n)={my(t=10^(n+1)\9*7); forvec(v=[[-1, n], [-7, -1]], ispseudoprime(p=t+10^(n-v[1])*v[2]) && return(p)); error} \\ M. F. Hasler, Feb 22 2016
Formula
a(n) = prime(A037066(n)). - Amiram Eldar, Jul 21 2025
Extensions
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
More terms from and a(0) = 2 prepended by M. F. Hasler, Feb 22 2016
Comments