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A269260
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For index k = A269230(n), the least prime with k consecutive digits 0, divided by 10^(k+1) and rounded down.
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4
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19, 10, 16, 16, 20, 30, 20, 15, 30, 26, 23, 27, 19, 17, 40, 30, 13, 13, 13, 24, 28, 22, 20, 10, 20, 30, 16, 10, 40, 13, 16, 11, 39, 10, 20, 20, 30, 10, 23, 16, 15, 30, 34, 56, 19, 28, 20, 20, 30, 20, 20, 90, 87, 68, 20, 25, 20, 16, 30, 40
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OFFSET
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1,1
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COMMENTS
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For indices k not listed in A269230, the least prime with k digits '0', A037053(k), has these digits consecutively, in a single run. If k is listed in A269230, this is not the case (e.g., A037053(32) = 10...0603), and the most economical way to make a prime with k consecutive digits 0 is to put two (a priori nonzero) digits in front of the string of k '0's, i.e., p = a*10^(k+1) + b with a > 9.
This sequence lists these numbers a, and the corresponding prime (least prime with k consecutive digits 0) is simply nextprime(a*10^(k+1)).
If a is a multiple of 10, then b can have two nonzero digits, 11 <= b <= 99. Otherwise (b < 10), this prime is also the least prime with k+1 (consecutive) digits '0', A037053(k+1), and k+1 is listed in A085824 (unless a > 90). It is then obviously not the smallest prime with *exactly* k consecutive digits 0, but with *at least* k consecutive digits 0. This happens for (n,k,a,b) = (2,43,10,9), (24,108,10,7), (28,121,10,3), (34,132,10,7), (38,144,10,9), ...
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LINKS
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PROG
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(PARI) A269260(n, k=A269230(n))=for(a=1, 9e9, nextprime(a*10^(k+1))-a*10^(k+1)<10^(valuation(a, 10)+1)&&return(a)) \\ If the 2nd (optional) arg is given, the 1st arg 'n' is ignored. Otherwise the function A269230() must be defined.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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