A376693 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.
1, 4, 15, 22, 39, 33, 291, 23174, 90137, 119135, 1641362, 1641337, 7113362, 471779113
Offset: 0
Examples
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.
Programs
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Maple
f:= proc(n) local x,i; x:= n; for i from 0 do if numtheory:-bigomega(x) <> 2 then return i fi; x:= x + convert(convert(x,base,10),`+`); od end proc: V:= Array(0..12): count:= 0: for i from 1 while count < 13 do v:= f(i); if v <= 12 and V[v] = 0 then V[v]:= i; count:= count+1 fi od: convert(V,list);
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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
Extensions
a(13) from Daniel Suteu, Nov 03 2024