A229469 Numbers k such that T(k) + S(k) + 1 is prime, where T(k) and S(k) are the k-th triangular and square numbers.
1, 5, 8, 9, 12, 17, 21, 24, 29, 32, 41, 44, 45, 53, 56, 57, 60, 68, 69, 77, 81, 84, 89, 92, 96, 108, 113, 117, 120, 132, 144, 149, 156, 164, 185, 197, 200, 201, 212, 213, 224, 233, 236, 248, 252, 260, 264, 269, 281, 288, 300, 312, 317, 321, 324, 329, 344, 353
Offset: 1
Examples
a(4)=9: T(9)+S(9)+1= 9/2*(9+1)+9^2+1= 127 which is prime. a(5)=12: T(12)+S(12)+1= 12/2*(12+1)+12^2+1= 223 which is prime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
-
Maple
KD:= proc() local a,b,c,d; a:= n/2*(n+1)+n^2+1; if isprime(a) then RETURN(n): fi; end: seq(KD(),n=1..5000);
-
PARI
v=List(); for(n=1, 10^5, if(isprime(n/2*(n+1)+n^2+1), listput(v, n))); Vec(v)
-
PARI
is(n)=isprime(n*(3*n+1)/2+1) \\ Charles R Greathouse IV, Sep 24 2013