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A063131
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Odd composite numbers which in base 2 contain their largest proper factor as a substring of digits.
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3
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55, 91, 215, 407, 493, 893, 1189, 1343, 1403, 1643, 1681, 1961, 3151, 3223, 3415, 4063, 4579, 7087, 7597, 7979, 8791, 9167, 10579, 11227, 13303, 13655, 14219, 15487, 16147, 22939, 23479, 24341, 25751, 26101, 27571, 28757, 30461, 30607
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OFFSET
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1,1
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COMMENTS
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The Pascal program checks to n=100000 in about a second on a 2GHz desktop, about three times as fast than the Mathematica program.
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LINKS
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MATHEMATICA
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Do[ If[ !PrimeQ[ n ] && StringPosition[ ToString[ FromDigits[ IntegerDigits[ n, 2 ] ] ], ToString[ FromDigits[ IntegerDigits[ Divisors[ n ] [ [ -2 ] ], 2 ] ] ] ] != {}, Print[ n ] ], {n, 3, 500, 2} ]
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PROG
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(Pascal) program A063131; var n, nn, lpd:longint; nstr, dstr:string; function prime(n:longint; var d:longint):boolean; var sq, i:longint; begin{PRIME} sq := round(sqrt(n)); for i := 2 to sq do if n mod i=0 then begin d := n div i; prime := false; exit; end; prime := true; end{PRIME}; begin{MAIN} for n := 3 to 100000 do if (n mod 2=1) and (not prime(n, lpd)) then begin nn := n; nstr := ''; repeat if nn mod 2=1 then nstr := '1'+nstr else nstr := '0'+nstr; nn := nn div 2; until nn=0; dstr := ''; repeat if lpd mod 2=1 then dstr := '1'+dstr else dstr := '0'+dstr; lpd := lpd div 2; until lpd=0; if pos(dstr, nstr)>0 then write(n:8); end; end.
(Magma) [k:k in [3..31000 by 2] | not IsPrime(k) and IntegerToString(Seqint(Intseq(Max(Set(Divisors(k)) diff {k}), 2))) in IntegerToString(Seqint(Intseq(k)), 2)]; // Marius A. Burtea, Jan 29 2020
(Python)
from sympy import divisors, isprime
def ok(n):
if n < 4 or n&1 == 0 or isprime(n): return False
return bin(divisors(n)[-2])[2:] in bin(n)[2:]
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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