A344891 - OEIS

%I #17 Sep 05 2023 12:22:04

%S 3,2,11,7,5,29,23,19,17,13,59,53,47,43,41,37,31,107,103,101,97,89,83,

%T 79,73,71,67,61,179,173,167,163,157,151,149,139,137,131,127,113,109,

%U 271,269,263,257,251,241,239,233,229,227,223,211,199,197,193,191,181

%N Divide the primes into subsets of lengths given by successive primes, then reverse the order of terms in each subset.

%C Irregular triangle read by rows in which row n lists the next p primes in decreasing order, where p is the n-th prime, with n >= 1.

%H Harvey P. Dale, <a href="/A344891/b344891.txt">Table of n, a(n) for n = 1..1000</a>

%e Written as an irregular triangle in which row lengths give A000040 the sequence begins:

%e     3,   2;

%e    11,   7,   5;

%e    29,  23,  19,  17,  13;

%e    59,  53,  47,  43,  41,  37,  31;

%e   107, 103, 101,  97,  89,  83,  79,  73,  71,  67,  61;

%e   179, 173, 167, 163, 157, 151, 149, 139, 137, 131, 127, 113, 109;

%e   ...

%t Module[{nn=10,p},p=Total[Prime[Range[nn]]];Flatten[Reverse/@TakeList[ Prime[ Range[ p]],Prime[Range[nn]]]]] (* _Harvey P. Dale_, Sep 14 2022 *)

%Y Right border gives A180302.

%Y Row lengths give A000040.

%Y Row products give A119645.

%Y Row sums give A034958.

%Y Cf. A343809.

%K nonn,tabf

%O 1,1

%A _Paolo Xausa_, Jun 01 2021