A115160 Numbers that are not the sum of two triangular numbers and a fourth power.

33, 63, 75, 125, 365, 489, 492, 684, 693, 723, 954, 1043, 1185, 1505, 1623, 1629, 1736, 1775, 1899, 1904, 1925, 2015, 2051, 2679, 2883, 3534, 3774, 3936, 4332, 4461, 4739, 4923, 5445, 5721, 5847, 6285, 6348, 6474, 6783, 7034, 7478, 8604, 9576, 9686, 9863

Offset: 1

Author

Giovanni Resta, Jan 15 2006

Keywords

• nonn

Comments

There are 88 such numbers up to 2*10^9, the last one in this range being 1945428.

Links

• David W. Wilson, Table of n, a(n) for n = 1..88

Crossrefs

Cf. A022552, A014158, A115159, A115161, A115162, A115163.

Programs

PARI

sumset_lim(a,b,lim)=my(v=[],u,t);if(a==b,for(i=1,#a,u=List();for(j=i,#b,t=a[i]+b[j];if(t>lim,break);listput(u,t));v=vecsort(concat(v,Vec(u)),,8)),for(i=1,#a,u=List();for(j=1,#b,t=a[i]+b[j];if(t>lim,break);listput(u,t));v=vecsort(concat(v,Vec(u)),,8)));v
makev(lim)=my(n=floor(sqrt(2*lim)-1/2),v);sumset_lim(v=vector(n,k,k*(k-1)/2),v,lim)
is(n)=for(i=1,#v,if(ispower(n-v[i],4),return(0));if(v[i]>n,return(1)))
v=makev(1e5);
for(n=1,1e5,if(is(n),print1(n", "))) \\ Charles R Greathouse IV, Aug 17 2011