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A348266
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k-digit numbers whose digit(s) are the number of distinct prime factors in each of the preceding k integers.
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2
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22, 313, 2232, 2323, 2333, 32215, 432152, 2434332, 4222423, 43332543, 332325334, 2535332433, 4532543535234, 5435433351423
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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 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.
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MATHEMATICA
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Select[Range[33000], FromDigits[PrimeNu /@ (# - Range[IntegerLength[#], 1, -1])] == # &] (* Amiram Eldar, Oct 09 2021 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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