A281577 Irregular triangle read by rows: T(n, k) = A281576(n) modulo p^2, where p is the k-th prime factor of A281576(n) with p < sqrt(A281576(n)).

28204, 17161560961, 2451293172821355028751076998879853, 1409441895293467096954080352837, 1385195550582, 17782786311867894562037823351528977990025091057921642664123352687840735480821116989430796689072791

Offset: 1

Author

Felix Fröhlich, Jan 24 2017

Keywords

• nonn
• tabf

Comments

The question whether T(n, k) = 0 for any values of n and k is an open problem (see Ribenboim p. 64, open problem (3)).

Examples

			Triangle T(n, k) starts
                                  28204
                            17161560961
     2451293172821355028751076998879853
        1409441895293467096954080352837
                 1385195550582, T(5, 2)
Note: T(5, 2) is not displayed here due to its size. The term can be seen in the Data section.
		

References

• P. Ribenboim, The Little Book of Bigger Primes, Springer Verlag, 1991.

Crossrefs

Cf. A050922, A281576.

Programs

PARI

a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
row(n) = my(i=0, k=1); while(1, if(a152155(k)!=-1, i++); if(i==n, forprime(p=1, sqrtint(2^(2^k)+1), if(Mod(2, p)^(2^k)==-1, print1(lift(Mod(2, p^2)^(2^k))+1, ", ")))); k++)
trianglerows(n) = for(k=1, n, row(k); print(""))