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

0,2

Links

Table of n, a(n) for n=0..13.

Example

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.

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);

Prog

(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

Crossrefs

Cf. A001358, A062028, A090009, A108638.

Sequence in context: A055465 A209870 A167293 * A267769 A192201 A054308

Adjacent sequences: A376690 A376691 A376692 * A376694 A376695 A376696

Keyword

nonn,base,more

Author

Robert Israel, Oct 01 2024

Extensions

a(13) from Daniel Suteu, Nov 03 2024

Status

approved