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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
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 (list; graph; refs; listen; history; text; internal format)
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 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

LINKS

Table of n, a(n) for n=2..70.

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

Cf. A032702.

Sequence in context: A333025 A144518 A051542 * A003079 A334119 A205128

Adjacent sequences:  A083657 A083658 A083659 * A083661 A083662 A083663

KEYWORD

nonn,base

AUTHOR

Farideh Firoozbakht, Jun 14 2003

EXTENSIONS

Terms verified by Alonso del Arte, Dec 09 2009

STATUS

approved

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Last modified October 28 13:26 EDT 2020. Contains 338055 sequences. (Running on oeis4.)