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

1,2

Comments

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

Links

Harry Metrebian, Table of n, a(n) for n = 1..65

Dario Alejandro Alpern, Brilliant numbers

Example

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

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}]

Crossrefs

Cf. A078972, A084475.

Sequence in context: A267455 A138249 A181604 * A289413 A247584 A049173

Adjacent sequences: A084473 A084474 A084475 * A084477 A084478 A084479

Keyword

base,hard,nonn

Author

Robert G. Wilson v, Jun 27 2003

Status

approved