A348266 k-digit numbers whose digit(s) are the number of distinct prime factors in each of the preceding k integers.

22, 313, 2232, 2323, 2333, 32215, 432152, 2434332, 4222423, 43332543, 332325334, 2535332433, 4532543535234, 5435433351423

Offset: 1

Author

Metin Sariyar, Oct 09 2021

Keywords

• nonn
• base
• more

Comments

a(12) <= 2535332433. - David A. Corneth, Oct 10 2021

a(12) >= 10^9. - Michel Marcus, Oct 11 2021

Examples

			22 is a term because omega(20) = 2 and omega(21) = 2, whose concatenation is 22.
313 is a term because preceding it omega(310) = 3, omega(311) = 1 and omega(312) = 3, and their concatenation is 313.
32215 is a 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.
		

Crossrefs

Cf. A001221, A000961, A007774, A033992, A033993, A051270, A074969, A176655.

Cf. A323083.

Programs

Mathematica

Select[Range[33000], FromDigits[PrimeNu /@ (# - Range[IntegerLength[#], 1, -1])] == # &] (* Amiram Eldar, Oct 09 2021 *)

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++;);}
lista(nn) = my(nb); for(n=1, nn, if (nb=isok(n), print1(n+nb, ", "))); \\ Michel Marcus, Oct 09 2021

Extensions

a(8)-a(9) from Amiram Eldar, Oct 09 2021

a(10)-a(11) from Michel Marcus, Oct 10 2021

a(12) confirmed by Martin Ehrenstein, Oct 28 2021

a(13)-a(14) from Martin Ehrenstein, Oct 30 2021