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

0,1

Comments

For n > 1, the last digit of n cannot be 5, therefore a(n) must have at least n+1 digits. It is probable that none among [10^n/9]*50 + {1,3,7,9} is prime in which case a(n) must have n+2 digits. We conjecture that for all n > 1, a(n) equals [10^(n+1)/9]*50 + b with 1 <= b <= 9 and one of the (first) digits 5 replaced by a 0, 1, 2, 3 or 4. - M. F. Hasler, Feb 22 2016

Links

M. F. Hasler, Table of n, a(n) for n = 0..200

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}]

Prog

(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

Crossrefs

Cf. A065588, A037062, A034388, A036507-A036536.

Cf. A037053, A037055, A037057, A037059, A037061, A037065, A037067, A037069, A037071.

Sequence in context: A081296 A133378 A283561 * A068105 A065588 A208277

Adjacent sequences: A037060 A037061 A037062 * A037064 A037065 A037066

Keyword

nonn,base

Author

Patrick De Geest, Jan 04 1999

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

Status

approved