cp's OEIS Frontend

A372009 Indices k such that A124652(k) is prime.

%I A372009 #19 May 05 2024 19:52:56
%S A372009 2,3,5,11,12,20,24,28,29,33,42,43,53,58,67,78,93,98,104,105,109,112,
%T A372009 118,125,126,137,141,145,146,162,174,182,185,187,188,195,200,223,224,
%U A372009 231,232,239,246,249,252,255,259,264,271,275,283,286,287,296,298,300,326
%N A372009 Indices k such that A124652(k) is prime.
%C A372009 Analogous to A111238, a sequence which instead pertains to A109890.
%H A372009 Michael De Vlieger, <a href="/A372009/b372009.txt">Table of n, a(n) for n = 1..2500</a>
%H A372009 Michael De Vlieger, <a href="/A372009/a372009.png">Log log scatterplot of A124652(n)</a>, n = 1..25000, showing primes in red.
%F A372009 Proper subset of A372028.
%e A372009 Let b(x) = A124652(x).
%e A372009 Table of first terms.
%e A372009    n  a(n)  b(a(n))
%e A372009   -----------------
%e A372009    1    2      2
%e A372009    2    3      3
%e A372009    3    5      5
%e A372009    4   11     11
%e A372009    5   12      7
%e A372009    6   20     31
%e A372009    7   24     13
%e A372009    8   28     19
%e A372009    9   29     17
%e A372009   10   33     37
%e A372009   11   42     29
%e A372009   12   43     41
%e A372009   ...
%t A372009 nn = 300; c[_] := False;
%t A372009 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A372009 f[x_] := Select[Range[x], Divisible[x, rad[#]] &];
%t A372009 Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];
%t A372009 {2}~Join~Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &];
%t A372009     If[PrimeQ[k], Sow[i]]; c[k] = True;
%t A372009     s += k, {i, 3, nn}] ][[-1, 1]]
%Y A372009 Cf. A124652, A372028, A372284.
%K A372009 nonn
%O A372009 1,1
%A A372009 _Michael De Vlieger_, Apr 29 2024