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%I #8 Feb 06 2017 03:45:29
%S 4,7,9,14,22,42,43,48,52,67,69,72,87,114,144,157,159,169,357,402,489,
%T 507,939,952,1029
%N Numbers that are not triangular numbers and cannot be written as the sum of a triangular number and two odd squares.
%C The sequence is conjectured to be complete (cf. Sun, 2009, Conjecture 1.2 (ii)).
%H Zhi-Wei Sun, <a href="https://www.novapublishers.com/catalog/product_info.php?products_id=18027">On sums of primes and triangular numbers</a>, Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2009), 65-76 (Article 6), [arXiv:0803.3737 [math.NT], 2009].
%o (PARI) list(lim)=my(v=List(),u=vectorsmall(lim\=1),s,t); forstep(a=1,sqrtint(lim),2, my(a2=a^2); forstep(b=1,min(sqrtint(lim-a2),a),2, t=a2+b^2; my(k=0); while((s=t+k*(k+1)/2)<=lim,u[s]=1;k++))); t=1; while((s=t*(t+1)/2)<=lim, u[s]=1; t++); for(i=1,lim, if(u[i]==0, listput(v,i))); Vec(v) \\ _Charles R Greathouse IV_, Feb 05 2017
%Y Cf. A000217, A016754, A141273.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Feb 05 2017