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 A083660 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. 1

%I

%S 1,5,14,5,5,9,1,1,29,23,28,13,46,22,18,116,35,18,155,7,81,1,139,52,

%T 262,215,56,29,11,6,256,119,381,592,67,189,116,46,5,275,139,27,101,

%U 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

%N 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.

%C Firoozbakht's conjecture: there exists an a(n) for every n greater than 1 and it is less than n^2.

%C For n with one digit, the searched-for prime must have at least 2n - 1 digits in base 10.

%C 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

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8</a> (www.primepuzzles.net).

%e 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.

%t (*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}]

%Y Cf. A032702.

%K nonn,base

%O 2,2

%A _Farideh Firoozbakht_, Jun 14 2003

%E Terms verified by _Alonso del Arte_, Dec 09 2009

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Last modified December 4 15:27 EST 2020. Contains 338927 sequences. (Running on oeis4.)