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A281621
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The smallest of four consecutive odd numbers with binary representations which, read in decimal, are prime.
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1
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173599, 418727, 1120979, 1283423, 1660677, 2755429, 3884515, 4704667, 5050711, 5058587, 5197757, 6613127, 6983139, 7423731, 10052677, 10311443, 11315237, 11769187, 15186613, 16145627, 18620507, 19579079, 19624723, 20823831, 20929957, 21387095, 21606883, 23517507
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 173599 is the smallest in set of 4 consecutive odd numbers {173599, 173601, 173603, 173605} whose binary representations respectively are {101010011000011111, 101010011000100001, 101010011000100011, 101010011000100101} which are all prime when read in decimal.
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MATHEMATICA
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Select[Range[-1, 30000001, 2], PrimeQ[FromDigits[IntegerDigits[(#), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 2), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 4), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 6), 2]]] &]
Select[Partition[Range[1, 23518000, 2], 4, 1], AllTrue[ FromDigits[ #]&/@ IntegerDigits[#, 2], PrimeQ]&][[All, 1]] (* Harvey P. Dale, Aug 30 2021 *)
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PROG
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(PARI) has(n)=isprime(fromdigits(binary(n), 10))
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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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