A187431 Numbers n that generate 5 primes under the first 5 iterations of the map n->A002731(n).

30131199, 50817201, 56496039, 74316929, 171407609, 276672151, 293315671, 337876949, 356498179, 359830101, 372590921, 432448789, 501182201, 541961069, 577016839, 616411051, 749536461, 776113741, 903321909, 919203811, 1005047121, 1285328811, 1323139751, 1340738371

Offset: 1

Author

Zak Seidov, Apr 05 2011

Keywords

• nonn

Comments

Numbers n such that m=(n^2+1)/2, p=(m^2+1)/2, q=(p^2+1)/2, r=(q^2+1)/2 and s=(r^2+1)/2 are all prime.

Subsequence of A188547 which itself is subsequence of A188546 which is subsequence of A116945.

a(1)=30131199=A188547(70).

Two numbers n that generate 6 primes... are a(23)=1323139751 and a(78)=10185588801.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..405, replacing an earlier b-file from Zak Seidov
• Stephan Baier, On the Bateman-Horn conjecture, Journal of Number Theory 96, 432-448 (2002).
• Paul T. Bateman, Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962) 363-367.

Crossrefs

Cf. A002731, A105318, A116945, A188546, A188547.