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 A238455 Difference between 4^n and the nearest triangular number. 2
 0, 1, 1, -2, 3, -11, 1, -87, -167, -306, -500, -552, 688, -3041, -579, 20854, 37075, 55618, 37108, -222296, -147729, 891994, 602155, -3523022, -2228805, 14811346, 11792251, -47737262, -1136517, 375078994, 741065851, 1445763154, 2746052116, 4910207464, 7492827856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 EXAMPLE a(0) = 1 - 1 = 0. a(1) = 4 - 3 = 1. a(2) = 16 - 15 = 1. a(3) = 64 - 66 = -2. a(4) = 256 - 253 = 3. MATHEMATICA db4n[n_]:=Module[{c=4^n, tr, t1, t2, d1, d2}, tr=Floor[(Sqrt[8c+1]-1)/2]; t1= (tr (tr+1))/ 2; t2=((tr+1)(tr+2))/2; d1=c-t1; d2=c-t2; If[d1> 1)     while a < sr*sr:  sr>>=1     b = sr>>1     while b:         s = sr + b         if a >= s*s:  sr = s         b>>=1     return sr for n in range(77):     nn = 4**n     s = isqrt(2*nn)     if s*(s+1)/2 > nn:  s-=1     d1 = nn - s*(s+1)/2     d2 = (s+1)*(s+2)/2 - nn     if d2 < d1:  d1 = -d2     print str(d1)+', ', (PARI) a(n) = {pow = 4^n; ft = floor((sqrt(8*pow+1) - 1)/2); df = pow - ft*(ft+1)/2; dc = pow - (ft+1)*(ft+2)/2; if (abs(df) > abs(dc), dc, df); } \\ Michel Marcus, Feb 27 2014 CROSSREFS Absolute values give the other bisection of A233327. Cf. A000079, A000217. Sequence in context: A070239 A002443 A111788 * A098929 A073098 A201267 Adjacent sequences:  A238452 A238453 A238454 * A238456 A238457 A238458 KEYWORD sign AUTHOR Alex Ratushnyak, Feb 26 2014 STATUS approved

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Last modified April 5 10:28 EDT 2020. Contains 333239 sequences. (Running on oeis4.)