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A347818
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Smallest n-digit brilliant number.
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0
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4, 10, 121, 1003, 10201, 100013, 1018081, 10000043, 100140049, 1000000081, 10000600009, 100000000147, 1000006000009, 10000000000073, 100000380000361, 1000000000000003, 10000001400000049, 100000000000000831, 1000000014000000049, 10000000000000000049, 100000000380000000361
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OFFSET
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1,1
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COMMENTS
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A brilliant number is a semiprime (products of two primes, A001358) whose two prime factors have the same number of decimal digits. For an n-digit brilliant number, the two prime factors must each have ceiling(n/2) decimal digits.
Since all brilliant numbers are semiprimes, a(n) >= A098449(n), also, a(n) = A098449(n) for n = 1, 2, 4, 16, 78, ..., are there infinitely many n such that a(n) = A098449(n)?
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LINKS
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FORMULA
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EXAMPLE
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a(6) = 100013 = 103 * 971.
a(7) = 1018081 = 1009 * 1009.
a(8) = 10000043 = 2089 * 4787.
a(9) = 100140049 = 10007 * 10007.
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MATHEMATICA
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Join[{4, 10}, Table[Module[{k=1}, While[PrimeOmega[10^n+k]!=2||Length[ Union[ IntegerLength/@ FactorInteger[ 10^n+k][[;; , 1]]]]!=1, k+=2]; 10^n+k], {n, 2, 20}]] (* Harvey P. Dale, Jan 09 2024 *)
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PROG
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(PARI) isA078972(n)=my(f=factor(n)); (#f[, 1]==1 && f[1, 2]==2) || (#f[, 1]==2 && f[1, 2]==1 && f[2, 2]==1 && #Str(f[1, 1])==#Str(f[2, 1]))
A084476(n)=for(k=0, 10^n, if(isA078972(10^(2*n-1)+k), return(k)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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