A175270 - OEIS

%I #12 Mar 17 2022 13:39:07

%S 0,1,2,13,14,18,19,20,29,33,34,35,36,37,44,54,58,59,61,62,65,72,73,75,

%T 77,86,90,96,97,101,106,107,118,129,130,131,134,137,138,140,146,147,

%U 148,152,155,157,158,160,161,164,166,176,179,181,184,187,193,195,200

%N Numbers k such that the least number of squares that add up to k equals the least number of triangular numbers that add up to k. Equivalently, A002828(k) = A061336(k).

%H Charles R Greathouse IV, <a href="/A175270/b175270.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) is2s(n)=my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, if(bitand(f[i, 2], 1) && bitand(f[i, 1], 3)==3, return(0))); 1

%o is2t(n)=my(m9=n%9,f); if(m9==5 || m9==8, return(0)); is2s(4*n+1)

%o is(n)=my(o2=valuation(n, 2),f); if(n==0, return(1)); if(bitand(o2, 1)==0 && bitand(n>>o2, 7)==7, return(0)); if(issquare(n), return(ispolygonal(n,3))); if(ispolygonal(n,3), return(0)); is2t(n)==is2s(n) \\ _Charles R Greathouse IV_, Mar 17 2022

%Y Cf. A000217, A000290, A002828, A061336.

%K nonn,easy

%O 1,3

%A _Ctibor O. Zizka_, Mar 19 2010

%E Data corrected and extended by _Mohammed Yaseen_, Mar 17 2022