cp's OEIS Frontend

A319282 Numbers of the form 16^i*(16*j + 15).

%I A319282 #17 Feb 18 2025 08:59:15
%S A319282 15,31,47,63,79,95,111,127,143,159,175,191,207,223,239,240,255,271,
%T A319282 287,303,319,335,351,367,383,399,415,431,447,463,479,495,496,511,527,
%U A319282 543,559,575,591,607,623,639,655,671,687,703,719,735,751,752,767,783,799,815
%N A319282 Numbers of the form 16^i*(16*j + 15).
%C A319282 {-a(n)} gives all negative fourth powers modulo all powers of 2, that is, negative fourth powers over 2-adic integers.
%H A319282 Jianing Song, <a href="/A319282/b319282.txt">Table of n, a(n) for n = 1..9999</a> (all terms <= 150000)
%F A319282 a(n) = 15*n + O(log(n)).
%o A319282 (PARI) isA319282(n)= n\16^valuation(n, 16)%16==15
%o A319282 (Python)
%o A319282 def A319282(n):
%o A319282     def bisection(f,kmin=0,kmax=1):
%o A319282         while f(kmax) > kmax: kmax <<= 1
%o A319282         kmin = kmax >> 1
%o A319282         while kmax-kmin > 1:
%o A319282             kmid = kmax+kmin>>1
%o A319282             if f(kmid) <= kmid:
%o A319282                 kmax = kmid
%o A319282             else:
%o A319282                 kmin = kmid
%o A319282         return kmax
%o A319282     def f(x): return n+x-sum((((x>>(i<<2))-15)>>4)+1 for i in range(x.bit_length()>>2))
%o A319282     return bisection(f,n,n) # _Chai Wah Wu_, Feb 17 2025
%Y A319282 A125169 is a proper subsequence.
%Y A319282 Perfect powers over 2-adic integers:
%Y A319282 Squares: positive: A234000; negative: A004215 (negated);
%Y A319282 Cubes: A191257;
%Y A319282 Fourth powers: positive: A319281; negative: this sequence (negated).
%K A319282 nonn
%O A319282 1,1
%A A319282 _Jianing Song_, Sep 16 2018