A037063 Smallest prime containing exactly n 5's.
2, 5, 557, 5557, 155557, 555557, 15555557, 55555553, 3555555551, 5555555557, 525555555557, 555555555551, 5555555555551, 355555555555559, 555555555555557, 51555555555555551, 545555555555555551, 555555555555555559, 15555555555555555557, 155555555555555555551
Offset: 0
Links
- M. F. Hasler, Table of n, a(n) for n = 0..200
Crossrefs
Programs
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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, 5], {n, 1, 18}] -
PARI
A037063(n)={my(p, t=10^(n+1)\9*50); n>1 && forvec(v=[[-1, n], [-5, -1]], nextprime(p=t+10^(n-v[1])*v[2])-p<10 && return(nextprime(p)));1+4^n} \\ M. F. Hasler, Feb 22 2016
Formula
a(n) = prime(A037062(n)). - Amiram Eldar, Jul 21 2025
Extensions
More terms from Randall L Rathbun, Jan 11 2002
Edited and corrected by Robert G. Wilson v, Jul 04 2003
More terms and a(0) = 2 from M. F. Hasler, Feb 22 2016
Comments