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Search: id:A074830
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| A074830 |
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Number of base reversals which result in a prime for bases less than n. |
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+0
1
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| 0, 0, 1, 0, 3, 2, 5, 2, 1, 3, 7, 3, 10, 4, 3, 3, 12, 4, 9, 5, 4, 7, 14, 4, 11, 5, 5, 7, 15, 3, 20, 9, 6, 6, 12, 3, 19, 11, 9, 6, 23, 4, 26, 8, 6, 10, 24, 7, 17, 11, 7, 15, 33, 4, 19, 9, 12, 12, 22, 5, 30, 16, 11, 13, 15, 4, 38, 15, 14, 8, 36, 5, 40, 17, 7, 13, 32, 4, 39, 13, 6, 13, 38, 4, 25
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OFFSET
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1,5
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COMMENT
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If n is composite, then there does not exist any bases greater than n for which its base reversal is prime. And if n is a prime, then there exists an infinite number of bases greater than n for which its base reversals are primes. Therefore the restriction to bases up to n only.
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EXAMPLE
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a(5) = 3 because 5 = 101 in base 2 and its reversal 101 base 2 = 5, 5 = 12 in base 3 and its reversal 21 base 3 = 7, 5 = 11 base 4 and its reversal 11 base 4 = 5. 3,7,&5 are all primes.
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MATHEMATICA
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f[n_] := Block[{c = 0, b = 2}, While[b < n + 1, If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], c++ ]; b++ ]; c]; Table[ f[n], {n, 1, 85}]
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CROSSREFS
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Sequence in context: A093527 A088233 A056008 this_sequence A127750 A112528 A154421
Adjacent sequences: A074827 A074828 A074829 this_sequence A074831 A074832 A074833
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KEYWORD
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base,easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 09 2002
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