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A084475 a(n) defines the first brilliant number, b_n, greater than 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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

STATUS

approved

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Last modified July 14 18:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)