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A080439
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a(1) = 11, a(n) = smallest prime obtained by inserting digits between every pair of digits of a(n-1).
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4
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OFFSET
| 1,1
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COMMENTS
| Conjecture: Only one digit needs to be inserted between each pair of digits of a(n-1) to get a(n); i.e. a(n) contains exactly 2n-1 digits for n > 1.
The conjecture above is false: a(5)=10000000000060571 has 17 digits instead of 2*5-1=9. A refined conjecture is: a(n) contains exactly 2^(n-1) + 1 digits for all n>0. This follows trivially by induction from the initial conjecture (above) of only one digit needed between each pair, and the fact that we start with 11, a 2 digit number, and holds true at least till a(12). [Julio Cesar Hernandez-Castro, Jul 05 2011]
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LINKS
| Julio Cesar Hernandez-Castro, Table of n, a(n) for n = 1..12
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EXAMPLE
| a(2) = 101 and a(3) is obtained by inserting a '0' and a '6' in the two inner spaces of 101: (1,-,0,-,1)
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MATHEMATICA
| a[n_] := Block[{d = IntegerDigits[n]}, k = Length[d]; While[k > 1, d = Insert[d, 0, k]; k-- ]; d = FromDigits[d]; e = d; k = 0; While[ !PrimeQ[e], k++; e = d + 10FromDigits[ IntegerDigits[k], 100]]; e]; NestList[a, 11, 6]
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CROSSREFS
| Cf. A080440, A080441, A080442, A080883 - A080914.
Sequence in context: A075767 A080176 A064490 * A098153 A020449 A089971
Adjacent sequences: A080436 A080437 A080438 * A080440 A080441 A080442
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KEYWORD
| nonn,base
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 22 2003
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EXTENSIONS
| Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2003
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