cp's OEIS Frontend

A381150 a(0) = 1, a(1) = 2, a(2) = 3; thereafter, a(n) = a(n-1) + (sum of prior prime terms or whose negatives are prime) - (sum of prior composite terms or whose negatives are composite).

%I A381150 #22 Feb 25 2025 09:44:12
%S A381150 1,2,3,8,5,7,16,9,-7,-30,-23,-39,-16,23,85,62,-23,-131,-370,-239,-347,
%T A381150 -802,-455,347,1496,1149,-347,-2190,-1843,347,2884,2537,-347,-3578,
%U A381150 -3231,347,4272,3925,-347,-4966,-4619,347,5660,5313,-347,-6354,-6007,-11667,-5660
%N A381150 a(0) = 1, a(1) = 2, a(2) = 3; thereafter, a(n) = a(n-1) + (sum of prior prime terms or whose negatives are prime) - (sum of prior composite terms or whose negatives are composite).
%H A381150 Michael De Vlieger, <a href="/A381150/b381150.txt">Table of n, a(n) for n = 0..10003</a> (a(n) for n = 1..1000 from James C. McMahon)
%H A381150 Michael De Vlieger, <a href="/A381150/a381150.png">Scatterplot of m*log_10(m*a(n))</a>, n = 1..2^10, where m = 1 of a(n) > 0 (shown in green) and m = -1 if a(n) < 0 (shown in red).
%H A381150 Michael De Vlieger, <a href="/A381150/a381150_1.png">Scatterplot of m*log_10(m*a(n))</a>, n = 1..2^16, where m = 1 of a(n) > 0 (shown in green) and m = -1 if a(n) < 0 (shown in red).
%e A381150 For n=5, a(5) = 5 + (2 + 3 + 5) - 8 = 7.
%e A381150 For n=9, a(9) = -7 + (2 + 3 + 5 + 7 -7) - (8 + 16 + 9) = -7 + 10 - 33 = -30
%p A381150 b:= proc(n) option remember; `if`(n<1, 0, b(n-1)+(t->
%p A381150      `if`(isprime(abs(t)), t, `if`(abs(t)>1, -t, 0)))(a(n)))
%p A381150     end:
%p A381150 a:= proc(n) option remember; `if`(n<3, n+1, a(n-1)+b(n-1)) end:
%p A381150 seq(a(n), n=0..48);  # _Alois P. Heinz_, Feb 15 2025
%t A381150 Nest[Append[#,#[[-1]]+Total[Select[#,PrimeQ]]-Total[Select[#,CompositeQ]]]&,{1,2,3},46]
%Y A381150 Cf. A000040, A002808, A101135,  A119746, A131093, A381149.
%K A381150 sign
%O A381150 0,2
%A A381150 _James C. McMahon_, Feb 15 2025