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Odd numbers which cannot be expressed as p + q*(q+1) where p and q are primes.
2

%I #21 Mar 31 2023 14:52:59

%S 1,3,5,7,21,27,39,45,51,57,81,105,111,141,147,171,177,231,273,303,315,

%T 351,357,471,501,525,567,585,735,741,761,771,831,849,861,897,945,1017,

%U 1083,1161,1197,1281,1343,1407,1475,1521,1525,1575,1695,1767,1997,2151

%N Odd numbers which cannot be expressed as p + q*(q+1) where p and q are primes.

%C It is conjectured that 1446377 is the largest term.

%C q*(q+1) is even which implies that p must be an odd prime.

%C The expression p + q*(q+1) resembles the expression p + 2*q used in Lemoine's conjecture.

%H Marc Ridders, <a href="/A360929/b360929.txt">Table of n, a(n) for n = 1..167</a>

%t a[1]=1;a[n_]:=a[n]=(k=a[n-1];c=True;While[c,k=k+2;c=False;q=2;While[!c&&q*(q+1)<k,p=k-(q*(q+1));c=PrimeQ[p];q=NextPrime[q]]];k);Table[a[n],{n,1,167}]

%Y Cf. A360930, A046927.

%K easy,nonn

%O 1,2

%A _Marc Ridders_, Feb 25 2023