|
%I #53 Nov 02 2021 06:27:33
%S 22,313,2232,2323,2333,32215,432152,2434332,4222423,43332543,
%T 332325334,2535332433,4532543535234,5435433351423
%N k-digit numbers whose digit(s) are the number of distinct prime factors in each of the preceding k integers.
%C a(12) <= 2535332433. - _David A. Corneth_, Oct 10 2021
%C a(12) >= 10^9. - _Michel Marcus_, Oct 11 2021
%e 22 is a term because omega(20) = 2 and omega(21) = 2, whose concatenation is 22.
%e 313 is a term because preceding it omega(310) = 3, omega(311) = 1 and omega(312) = 3, and their concatenation is 313.
%e 32215 is term because, the number of distinct prime divisors of 32210, 32211, 32212, 32213 and 32214 are 3, 2, 2, 1, 5 and their ordered concatenation gives the next number 32215.
%t Select[Range[33000], FromDigits[PrimeNu /@ (# - Range[IntegerLength[#], 1, -1])] == # &] (* _Amiram Eldar_, Oct 09 2021 *)
%o (PARI) isok(m) = {my(s="", k=m, i=1); while(1, s = concat(s, Str(omega(k))); if (eval(s) == m+i, return (i)); if (eval(s) > m+i, return(0)); k++; i++;);}
%o lista(nn) = my(nb); for(n=1, nn, if (nb=isok(n), print1(n+nb, ", "))); \\ _Michel Marcus_, Oct 09 2021
%Y Cf. A001221, A000961, A007774, A033992, A033993, A051270, A074969, A176655.
%Y Cf. A323083.
%K nonn,base,more
%O 1,1
%A _Metin Sariyar_, Oct 09 2021
%E a(8)-a(9) from _Amiram Eldar_, Oct 09 2021
%E a(10)-a(11) from _Michel Marcus_, Oct 10 2021
%E a(12) confirmed by _Martin Ehrenstein_, Oct 28 2021
%E a(13)-a(14) from _Martin Ehrenstein_, Oct 30 2021
|
