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 A257461 Let b_k=9...9 consist of k>0 9's. Then a(n) is the smallest k such that the concatenation prime(n)b_k is prime, or a(n)=0 if there is no such prime. 3
 1, 0, 1, 1, 5, 1, 1, 1, 1, 2, 28, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 3, 1, 2, 90, 1, 1, 2, 8, 2, 1, 1, 2, 1, 1, 2, 1, 4, 6, 8, 3, 2, 3, 4, 1, 1, 5, 1, 5, 60, 1, 1, 5, 6, 1, 2, 1, 1, 2, 1, 10, 1, 1, 1, 5, 2, 1, 3, 4, 1, 1, 2, 4, 1, 3, 4, 3, 2, 1, 1, 2, 1, 6, 1, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The only unknown terms less than 10000, tested to 25000, are for n: 87, 5744, 8041, 9533. For p(87)=449, the concatenation is divisible by 11 if k is odd and is divisible by 7 if k == 4 (mod 6). LINKS Table of n, a(n) for n=1..86. Vladimir Shevelev and Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found. FORMULA a(n)=k for the least k such that p(n)*10^k+10^k-1 is prime, where p(n) is the n_th prime. MATHEMATICA f[n_] := Block[{k = 1, p = Prime[n]}, While[ !PrimeQ[p*10^k + 10^k - 1], k++]; k]; f[2] = 0; Array[f, 86] CROSSREFS Cf. A257459, A232210, A257460. Sequence in context: A031261 A188796 A161685 * A129398 A109009 A060904 Adjacent sequences: A257458 A257459 A257460 * A257462 A257463 A257464 KEYWORD nonn,base AUTHOR Vladimir Shevelev and Robert G. Wilson v, Apr 24 2015 EXTENSIONS a(87) from Eric Chen, Apr 24 2015 STATUS approved

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Last modified September 12 19:09 EDT 2024. Contains 375853 sequences. (Running on oeis4.)