A084476 Least k such that 10^(2n-1)+k is a brilliant number.

0, 3, 13, 43, 81, 147, 73, 3, 831, 49, 987, 691, 183, 4153, 279, 667, 709, 277, 1687, 997, 1207, 91, 1411, 393, 951, 9793, 2217, 6229, 2317, 213, 399, 19, 2317, 609, 2607, 11901, 10563, 5473, 3, 5923, 17527, 8569, 16701, 11989, 9757, 6489, 3489, 2899

Offset: 1

Author

Robert G. Wilson v, Jun 27 2003

Keywords

• base
• hard
• nonn

Comments

Least brilliant number greater than 10^(2n) is {10^n+A033873(n)}^2. The web site also lists the two prime factors.

Examples

			a(3)=13 because 10^5+13 = 100013 = 103*971.
		

Links

• Harry Metrebian, Table of n, a(n) for n = 1..65
• Dario Alejandro Alpern, Brilliant numbers

Crossrefs

Cf. A078972, A084475.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; LengthBase10[n_] := Floor[ Log[10, n] + 1]; f[n_] := Block[{k = 0}, If[ EvenQ[n] && n > 1, NextPrim[ 10^(n/2)]^2 - 10^(n/2), While[fi = FactorInteger[10^n + k]; Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ fi] != 2 || Length[ Union[ LengthBase10 /@ Flatten[ Table[ # [[1]], {1}] & /@ fi]]] != 1, k++ ]; k]]; Table[ f[2n + 1], {n, 1, 24}]