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 A080442 a(1) = 19, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n-1). 4
 19, 109, 10009, 100000039, 10000000000002359, 100000000000000000000000002031519, 10000000000000000000000000000000000000000000000000002000301050179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: Only one digit needs to be inserted between each pair of digit 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) = 10000000000002359 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 from the initial conjecture of only one digit needed between each pair, and the fact that we start with 19, a 2-digit number, and holds true at least till a(12). - Julio Cesar Hernandez-Castro, Jul 07 2011 LINKS Julio Cesar Hernandez-Castro, Table of n, a(n) for n = 1..12 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, 19, 6] CROSSREFS Cf. A080439, A080440, A080441, A080883 - A080914. Sequence in context: A158715 A372010 A186105 * A033655 A245753 A164604 Adjacent sequences: A080439 A080440 A080441 * A080443 A080444 A080445 KEYWORD base,nonn AUTHOR Amarnath Murthy, Feb 22 2003 EXTENSIONS Edited and extended by Robert G. Wilson v, Feb 22 2003 STATUS approved

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Last modified August 8 10:02 EDT 2024. Contains 375019 sequences. (Running on oeis4.)