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A290078
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Where the ratio A235027(n)/n obtains record values.
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1
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1, 11, 19, 67, 71, 263, 271, 781, 1273, 1349, 2981, 4757, 5041, 18157, 18673, 19241, 55451, 71273, 73441, 95779, 211651, 337747, 357911, 1289147, 1325783, 1366111, 3937021, 5060383, 5214311, 6800309, 15027221, 19314983, 19902511, 23980037, 25411681
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OFFSET
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1,2
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COMMENTS
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Because A056539(n)/n < 2 for all n, and already for the tenth term of this sequence 1349 we have A235027(1349)/1349 = 2.094... it follows that the only primes present are terms a(2) .. a(7): 11, 19, 67, 71, 263, 271. Conjecture: every term after that is a product of some of those six primes. For example: 781 = 11*71, 1273 = 19*67, 1349 = 19*71, 2981 = 11*271, 4757 = 67*71, 5041 = 71*71.
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LINKS
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PROG
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(PARI)
revbits(n) = fromdigits(Vecrev(binary(n)), 2);
A235027(n) = {my(f = factor(n)); for (k=1, #f~, if (f[k, 1] != 2, f[k, 1] = revbits(f[k, 1]); ); ); factorback(f); } \\ This function from Michel Marcus, Aug 05 2017
m=0; i=0; n=0; while(i<35, n++; if((A235027(n)/n) > m, m = A235027(n)/n; i++; print1(n, ", ")));
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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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