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A083660
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Smallest nonnegative integer m such that the concatenation of the integers from n to 1 interspersed with those of m, in base 10, is prime.
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1
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1, 5, 14, 5, 5, 9, 1, 1, 29, 23, 28, 13, 46, 22, 18, 116, 35, 18, 155, 7, 81, 1, 139, 52, 262, 215, 56, 29, 11, 6, 256, 119, 381, 592, 67, 189, 116, 46, 5, 275, 139, 27, 101, 118, 96, 167, 196, 393, 275, 91, 146, 415, 193, 127, 85, 73, 6, 4, 50, 118, 1046, 362, 5, 431, 248, 180, 82, 230, 125
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OFFSET
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2,2
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COMMENTS
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Firoozbakht's conjecture: there exists an a(n) for every n greater than 1 and it is less than n^2.
For n with one digit, the searched-for prime must have at least 2n - 1 digits in base 10.
Firoozbakht's conjecture holds true up to at least 100. With adequately coded commands, verification should not take longer than a minute. - Alonso del Arte, Dec 09 2009
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LINKS
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C. Rivera, Puzzle 8 (www.primepuzzles.net).
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EXAMPLE
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a(4) = 14 because the concatenation of the digits from 4 to 1 (that is, 4321) with 14 stuck between each of them is 4143142141, and that is a prime number. Similar concatenations with numbers less than 14 used in 14's place all give composite numbers.
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MATHEMATICA
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(*In the absence of a base argument, the function leastGenPrimeByListingFNI assumes the base is 10. Minimum and maximum allowed base values are 2 and 36.*) leastGenPrimeByListingFNI[n_, b_: 10] := Module[{m = 0, p, flag = False}, While[Not[flag], m++; p = FromDigits[Flatten[{Table[{IntegerDigits[i, b], IntegerDigits[m, b]}, {i, n, 2, -1}], {1}}], b]; flag = PrimeQ[p]]; Return[m]]; Table[leastGenPrimeByListingFNI[n], {n, 2, 10}]
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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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EXTENSIONS
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STATUS
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approved
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