A290078 Where the ratio A235027(n)/n obtains record values.

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..35.

Index entries for sequences related to binary expansion of n

Prog

(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, ", ")));

Crossrefs

Cf. A235027.

Sequence in context: A080788 A363023 A248802 * A089032 A344042 A335410

Adjacent sequences: A290075 A290076 A290077 * A290079 A290080 A290081

Keyword

nonn,base

Author

Antti Karttunen, Aug 07 2017

Status

approved