A255904 Numbers that are neither triangular nor the sum of a positive triangular number and a prime.

2, 7, 61, 211, 216

Offset: 1

Author

Arkadiusz Wesolowski, Mar 10 2015

Keywords

• nonn
• fini

Comments

Probably finite.

First four terms are primes, and are in A065397.

If it exists, a(6) > 5*10^6. - Derek Orr, Mar 12 2015

If it exists, a(6) > 4*10^9. - Hiroaki Yamanouchi, Mar 16 2015

Examples

			a(2) = 7 is in the sequence because 7 is not a triangular number, and cannot be written as a sum of the primes < 7 {2, 3, 5} and one of the positive triangular numbers < 7 {1, 3, 6}.
		

Crossrefs

Cf. A065397, A076768.

Programs

Magma

lst:=[]; r:=21; for n in [0..r*(r+1)/2] do if not IsSquare(8*n+1) then f:=0; k:=1; while k*(k+1)/2 lt n-1 do if IsPrime(n-Truncate(k*(k+1)/2)) then f:=1; break; end if; k+:=1; end while; if IsZero(f) then Append(~lst, n); end if; end if; end for; lst;

PARI

a(n)=k=1;while(n-(t=k*(k+1)/2)>=0,if(isprime(n-t)||n==t,return(k));k++)
n=1;while(n<10^5,if(!a(n),print1(n,", "));n++) \\ Derek Orr, Mar 12 2015