A389915 Odd numbers m such that at least one of the factors of Stern polynomial B(m,x) has at least one negative coefficient.

63, 1023, 2079, 3087, 3591, 3843, 3969, 4095, 8001, 8127, 8235, 10881, 16065, 16191, 16383, 16401, 16779, 20475, 28665, 32193, 32319, 32767, 32835, 33787, 36855, 48771, 49665, 61425, 64449, 64575, 128961, 129087, 131103, 132111, 132615, 132867, 132993, 133119, 135135, 139167, 147231, 163359, 195615, 196623, 197127

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Example

The Stern polynomial B(63,t) (see A125184) is x^5 + x^4 + x^3 + x^2 + x + 1, which factorizes as (x+1)(x^2 - x + 1)(x^2 + x + 1), where second factor has a negative coefficient, therefore 63 is included in this sequence.

Prog

(PARI)
ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
is_A389915(n) = if(!(n%2), 0, my(p=ps(n), f=factor(p)); for(i=1, #f~, if(0>vecmin(Vec(f[i, 1])), return(1))); (0));

Crossrefs

Cf. A125184, A260443, A277013.

Subsequence of A389917.

Sequence in context: A112494 A258004 A258014 * A183076 A230660 A132465

Adjacent sequences: A389912 A389913 A389914 * A389916 A389917 A389918

Keyword

nonn

Author

Antti Karttunen, Dec 04 2025

Status

approved