A379350 - OEIS

A379350

Triangle read by rows in which row n lists numbers k such that the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

%I #14 Dec 22 2024 23:56:15

%S 0,1,2,4,5,22,3,8,14,19,140,7,10,24,41,58,265,707,6,13,25,32,44,63,

%T 146,184,602,3407,21362,11,30,52,71,112,194,298,481,503,2695,3433,

%U 4991,16,27,59,70,102,113,317,500,586,1048,2951,3424,4972,8240,12658,83834,686210,1306066

%N Triangle read by rows in which row n lists numbers k such that the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

%C For any prime p, there are finitely many x such that x^2 + 2 has p as its greatest prime factor.

%H Andrew Howroyd, <a href="/A379350/b379350.txt">Table of n, a(n) for n = 1..915</a> (first 21 rows for primes up to 193)

%H Filip Najman, <a href="http://web.math.hr/~fnajman/smooth.pdf">Smooth values of some quadratic polynomials</a>, Glasnik Matematicki Series III 45 (2010), pp. 347-355.

%H Filip Najman, <a href="https://web.math.pmf.unizg.hr/~fnajman/publications.html">List of Publications Page</a> (Adjacent to entry number 7 are links with a data file for rows 2..21 (=914 terms) of this sequence).

%e Irregular triangle begins:

%e p | {k}

%e -----+------------------

%e 2 | {0}

%e 3 | {1, 2, 4, 5, 22}

%e 11 | {3, 8, 14, 19, 140}

%e 17 | {7, 10, 24, 41, 58, 265, 707}

%e 19 | {6, 13, 25, 32, 44, 63, 146, 184, 602, 3407, 21362}

%e 41 | {11, 30, 52, 71, 112, 194, 298, 481, 503, 2695, 3433, 4991}

%e ...

%Y Cf. A033203, A379351, A379352 (first terms), A185397 (last terms), A379349 (row lengths).

%Y Cf. A223701, A223702, A242488.

%K nonn,tabf

%O 1,3

%A _Andrew Howroyd_, Dec 22 2024