

A080442


a(1) = 19, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n1).


4




OFFSET

1,1


COMMENTS

Conjecture: Only one digit needs to be inserted between each pair of digit of a(n1) to get a(n); i.e., a(n) contains exactly 2n1 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^(n1) + 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 2digit number, and holds true at least till a(12).  Julio Cesar HernandezCastro, Jul 07 2011


LINKS



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



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



