A037069 Smallest prime containing exactly n 8's.

2, 83, 881, 8887, 88883, 888887, 28888883, 88888883, 888888883, 48888888883, 288888888889, 888888888887, 48888888888883, 88888888888889, 888888888888883, 18888888888888883, 88888888888888889, 2888888888888888887, 8888888888888888881, 388888888888888888889

Offset

0,1

Comments

The last digit of n cannot be 8, therefore a(n) must have at least n+1 digits. It is probable (using [] for floor) that none among [10^n/9]*80 + {1,3,7,9} is prime in which case a(n) must have n+2 digits. We conjecture that for all n >= 0, a(n) equals [10^(n+1)/9]*80 + b with 1 <= b <= 9 and one of the (first) digits 8 replaced by a digit among {0, ..., 7}. - 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, 8], {n, 1, 18}]

Prog

(PARI) A037069(n)={my(p, t=10^(n+1)\9*80); forvec(v=[[-1, n], [-8, -1]], nextprime(p=t+10^(n-v[1])*v[2])-p<10 && return(nextprime(p)))} \\ ~

Crossrefs

Cf. A065591, A037068, A034388, A036507-A036536.

Cf. A037053, A037055, A037057, A037059, A037061, A037063, A037065, A037067, A037071.

Sequence in context: A175449 A371475 A171399 * A065591 A266201 A225807

Adjacent sequences: A037066 A037067 A037068 * A037070 A037071 A037072

Keyword

nonn,base,easy

Author

Patrick De Geest, Jan 04 1999

Extensions

Corrected by Jud McCranie, Jan 04 2001

More terms from Erich Friedman, Jun 03 2001

More terms and a(0) = 2 from M. F. Hasler, Feb 22 2016

Status

approved