

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



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

2,2


COMMENTS

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 searchedfor 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


LINKS

C. Rivera, Puzzle 8 (www.primepuzzles.net).


EXAMPLE

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.


MATHEMATICA

(*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}]


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



