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 A037069 Smallest prime containing exactly n 8's. 14
 2, 83, 881, 8887, 88883, 888887, 28888883, 88888883, 888888883, 48888888883, 288888888889, 888888888887, 48888888888883, 88888888888889, 888888888888883, 18888888888888883, 88888888888888889, 2888888888888888887, 8888888888888888881, 388888888888888888889 (list; graph; refs; listen; history; text; internal format)
 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)*v)-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: A108312 A175449 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

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Last modified September 29 12:44 EDT 2022. Contains 357090 sequences. (Running on oeis4.)