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A080440
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a(1) = 13, 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(4)=100000963 has 9 digits instead of 2*4-1=7. 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 above conjecture of only one digit needed between each pair, and the fact that we start with 13, a 2 digit number, and holds true at least till a(12). [Julio Cesar Hernandez-Castro, Jul 06 2011]
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LINKS
| Julio Cesar Hernandez-Castro, Table of n, a(n) for n = 1..12
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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, 13, 6]
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CROSSREFS
| Cf. A080439, A080441, A080442, A080883 - A080914.
Sequence in context: A066034 A100277 A087398 * A159352 A129762 A023011
Adjacent sequences: A080437 A080438 A080439 * A080441 A080442 A080443
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KEYWORD
| base,nonn
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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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