A080440 a(1) = 13, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n-1).

13, 103, 10093, 100000963, 10000000000092653, 100000000000000000000000902060523, 10000000000000000000000000000000000000000000000090002000600051233

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(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

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, 13, 6]

Crossrefs

Cf. A080439, A080441, A080442, A080883 - A080914.

Sequence in context: A240804 A100277 A087398 * A159352 A289859 A129762

Adjacent sequences: A080437 A080438 A080439 * A080441 A080442 A080443

Keyword

base,nonn

Author

Amarnath Murthy, Feb 22 2003

Extensions

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

Status

approved