A080439 a(1) = 11, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n-1).

11, 101, 10061, 100000651, 10000000000060571, 100000000000000000000000600052761, 10000000000000000000000000000000000000000000000060000000502271641

Offset

1,1

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

Links

Julio Cesar Hernandez-Castro, Table of n, a(n) for n = 1..12

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).

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]

Crossrefs

Cf. A080440, A080441, A080442, A080883 - A080914.

Sequence in context: A292014 A080176 A064490 * A098153 A020449 A089971

Adjacent sequences: A080436 A080437 A080438 * A080440 A080441 A080442

Keyword

nonn,base

Author

Amarnath Murthy, Feb 22 2003

Extensions

Edited, corrected and extended by Robert G. Wilson v, Feb 22 2003

Status

approved