A084475 - OEIS

%I #16 Jul 07 2023 21:15:08

%S 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,

%T 183,37,4153,31,279,37,667,61,709,3,277,3,1687,51,997,39,1207,117,91,

%U 9,1411,117,393,7,951,13,9793,67,2217,103,6229,331,2317,319,213,57,399,33,19

%N 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.

%H Harry Metrebian, <a href="/A084475/b084475.txt">Table of n, a(n) for n = 0..130</a>

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/BRILLIANT.HTM">Brilliant numbers</a>

%e 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).

%t 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}]

%Y Cf. A078972, A084476.

%K base,nonn

%O 0,1

%A _Jason Earls_, Jun 03 2003

%E Edited and extended by _Robert G. Wilson v_, Jun 27 2003