A376693 - OEIS

%I #10 Nov 07 2024 04:35:27

%S 1,4,15,22,39,33,291,23174,90137,119135,1641362,1641337,7113362,

%T 471779113

%N a(n) is the first k such that if x(1) = k and x(i+1) = A062028(x(i)), x(1) to x(n) are all semiprimes but x(n+1) is not.

%e a(4) = 39 because 39 = 3 * 13 is a semiprime, A062028(39) = 39 + 3 + 9 = 51 = 3 * 17 is a semiprime, A062028(51) = 51 + 5 + 1 = 57 = 3 * 19 is a semiprime, A062028(57) = 57 + 5 + 7 = 69 = 3 * 23 is a semiprime, but A062028(69) = 69 + 6 + 9 = 84 = 2^2 * 3 * 7 is not a semiprime.

%p f:= proc(n) local x,i;

%p x:= n;

%p for i from 0 do

%p   if numtheory:-bigomega(x) <> 2 then return i fi;

%p   x:= x + convert(convert(x,base,10),`+`);

%p od

%p end proc:

%p V:= Array(0..12): count:= 0:

%p for i from 1 while count < 13 do

%p   v:= f(i);

%p   if v <= 12 and V[v] = 0 then V[v]:= i; count:= count+1 fi

%p od:

%p convert(V,list);

%o (PARI) a(n) = if(n==0, return(1)); for(k=1, oo, if(bigomega(k) == 2, my(c=1, t=k+sumdigits(k)); while(bigomega(t) == 2, c += 1; t += sumdigits(t)); if(c == n, return(k)))); \\ _Daniel Suteu_, Nov 03 2024

%Y Cf. A001358, A062028, A090009, A108638.

%K nonn,base,more

%O 0,2

%A _Robert Israel_, Oct 01 2024

%E a(13) from _Daniel Suteu_, Nov 03 2024