|
%I #16 Jul 17 2021 11:24:13
%S 1,5,10,35,60,70,75,210,240,385,430,445,495,590,655,730,805,815,835,
%T 1005,1040,1045,1230,1390,1430,1530,1670,1715,1850,1890,1920,2000,
%U 2020,2100,2110,2245,2310,2405,2415,2495,2545,2685,2755,2840,2935,2950,3045,3255,3260,3335,3420,3650,3775,3805
%N Numbers k such that N = k^2 is a twin rank (cf. A002822: 6N +- 1 are twin primes).
%C Dinculescu notes that when k^2 > 1 is a twin rank (i.e., in A002822), then k is always a multiple of 5, and if k^3 > 1 is a twin rank, it is divisible by 7. See A326231 for the terms > 1 divided by 5.
%C See A326234 and A326233 for k^3, A326236 and A326235 for k^6.
%H A. Dinculescu, <a href="/A326232/b326232.txt">Table of n, a(n) for n = 1..10001</a>
%H A. Dinculescu, <a href="http://www.utgjiu.ro/math/sma/v13/p13_11.pdf">On the Numbers that Determine the Distribution of Twin Primes</a>, Surveys in Mathematics and its Applications, 13 (2018), 171-181.
%o (PARI) select( is(n)=!for(s=1,2,ispseudoprime(6*n^2+(-1)^s)||return), [1..5000])
%Y Cf. A002822, A326231 (a(n)/5, n>1), A326233, A326234 (analog for k^3), A326235, A326236 (analog for k^6), A326230 (least twin rank m^n for given n).
%K nonn
%O 1,2
%A _M. F. Hasler_ and _Antonie Dinculescu_, Jun 14 2019
|
