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A037063 Smallest prime containing exactly n 5's. 15
2, 5, 557, 5557, 155557, 555557, 15555557, 55555553, 3555555551, 5555555557, 525555555557, 555555555551, 5555555555551, 355555555555559, 555555555555557, 51555555555555551, 545555555555555551, 555555555555555559, 15555555555555555557, 155555555555555555551 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified November 19 06:26 EST 2019. Contains 329310 sequences. (Running on oeis4.)