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

Author

Antti Karttunen, Aug 07 2017

Keywords

• nonn
• base

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

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A235027.

Programs

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,",")));