A226072 -id:A226072 - cp's OEIS frontend

A226074 Numbers k such that k^2+1 is a triangular number and k^2+2 is a prime number.

0, 3, 105, 4116315, 9721683943673162520781155, 35285058531373239343849920668944097883186271103498415

Offset: 1

Alex Ratushnyak, May 25 2013

nonn

a(7) has 191 decimal digits: 222247847...170444715.
Corresponding primes and indices of triangular numbers: A226072 and A226073.
Subsequence of A106328. - Max Alekseyev, Jan 30 2014

Cf. A226069-A226073.

A226070 Numbers k such that k^2-1 is a triangular number and k^2+1 is a prime.

Original entry on oeis.org

1, 2, 4, 134, 2174, 154634

Offset: 1

Alex Ratushnyak, May 25 2013

Subsequence of A006452 that consists of the terms k such that k^2+1 is prime.

a(7) is too large to include here (see b-file). - Max Alekseyev, Jan 30 2014

Max Alekseyev, Table of n, a(n) for n = 1..12

Corresponding primes: A226069.
Indices of corresponding triangular numbers: A226071.
Cf. A226072-A226074.

C
```
// see A226069.
```

Select[Range[155000],PrimeQ[#^2+1]&&OddQ[Sqrt[8(#^2-1)+1]]&] (* Harvey P. Dale, Jul 19 2019 *)

Terms a(7)-a(12) from Max Alekseyev, Jan 30 2014

A226073 Numbers k such that triangular(k)-1 is a square and triangular(k)+1 is a prime number.

Original entry on oeis.org

1, 4, 148, 5821348, 13748537282247342677718148, 49900608324196518198677680899235165296598423281799348

Offset: 1

Alex Ratushnyak, May 25 2013

nonn

a(7) has 191 decimal digits: 314305920...194453348.

Corresponding primes and roots of squares: A226072 and A226074.

Cf. A226069-A226074.

cp's OEIS Frontend

A226074 Numbers k such that k^2+1 is a triangular number and k^2+2 is a prime number.

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A226070 Numbers k such that k^2-1 is a triangular number and k^2+1 is a prime.

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A226073 Numbers k such that triangular(k)-1 is a square and triangular(k)+1 is a prime number.

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