A229157 -id:A229157 - cp's OEIS frontend

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

K. D. Bajpai, Sep 24 2013

			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.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000217, A000290.

Cf. A228908, A229157.

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);

v=List(); for(n=1, 10^5, if(isprime(n/2*(n+1)+n^2+1), listput(v, n))); Vec(v)

is(n)=isprime(n*(3*n+1)/2+1) \\ Charles R Greathouse IV, Sep 24 2013

A229960 Primes of the form n^3 - T(n) - 1 where T(n) is the n-th triangular number.

Original entry on oeis.org

53, 109, 683, 4759, 7789, 9029, 13523, 15299, 45989, 63179, 68059, 90089, 116423, 174019, 225089, 370619, 610469, 700963, 994949, 1025149, 1119403, 1398599, 1594709, 1898873, 2291189, 2561899, 2734129, 2975543, 3038039, 3296773, 3784169, 3857489, 5913269, 6212483

Offset: 1

K. D. Bajpai, Oct 04 2013

Also primes of the form (2*n^3 - n^2 - n - 2)/2.

			a(2) = 109 since 5^3 - T(5) - 1 = 125 - 15 - 1 = 109, which is prime.
a(6) = 9029 since 21^3 - T(21) - 1 = 9261 - 231 - 1 = 9029 which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A229157, A229080.

KD:= proc() local a,b,d; a:= n^3;b:=(1/2)*n*(n+1); d:=a-b-1; if isprime(d) then   RETURN(d): fi;end: seq(KD(),n=1..500);

Select[Table[(n^3) - (n/2*(n + 1)) - 1, {n, 200}], PrimeQ]

cp's OEIS Frontend

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.

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