A084475 a(n) defines the first brilliant number, b_n, greater than or equal to 10^n. If n is odd or zero, then b_n is 10^n+a(n); and if n is a positive even number, then b_n is {10^(n/2)+a(n)}^2.

3, 0, 1, 3, 1, 13, 9, 43, 7, 81, 3, 147, 3, 73, 19, 3, 7, 831, 7, 49, 19, 987, 3, 691, 39, 183, 37, 4153, 31, 279, 37, 667, 61, 709, 3, 277, 3, 1687, 51, 997, 39, 1207, 117, 91, 9, 1411, 117, 393, 7, 951, 13, 9793, 67, 2217, 103, 6229, 331, 2317, 319, 213, 57, 399, 33, 19

Offset

0,1

Links

Harry Metrebian, Table of n, a(n) for n = 0..130

Dario Alejandro Alpern, Brilliant numbers

Example

a(5)=13 because 10^5+13 = 100013 = 103*971 and a(6)=9 because (10^3+9)^2 = 1009^2. For n>0, a(2n) = A033873(n).

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[n], {n, 0, 63}]

Crossrefs

Cf. A078972, A084476.

Sequence in context: A291960 A160052 A035650 * A130028 A129560 A218603

Adjacent sequences: A084472 A084473 A084474 * A084476 A084477 A084478

Keyword

base,nonn

Author

Jason Earls, Jun 03 2003

Extensions

Edited and extended by Robert G. Wilson v, Jun 27 2003

Name corrected by Sean A. Irvine, Apr 18 2026

Status

approved