A175270 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).

0, 1, 2, 13, 14, 18, 19, 20, 29, 33, 34, 35, 36, 37, 44, 54, 58, 59, 61, 62, 65, 72, 73, 75, 77, 86, 90, 96, 97, 101, 106, 107, 118, 129, 130, 131, 134, 137, 138, 140, 146, 147, 148, 152, 155, 157, 158, 160, 161, 164, 166, 176, 179, 181, 184, 187, 193, 195, 200

Offset: 1

Author

Ctibor O. Zizka, Mar 19 2010

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A000290, A002828, A061336.

Programs

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

Extensions

Data corrected and extended by Mohammed Yaseen, Mar 17 2022