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A328574 a(1) = 0, and, for n >= 2, numbers n whose primorial base expansion doesn't contain any nonleading zeros. 6

%I #23 Feb 16 2021 04:45:00

%S 0,1,3,5,9,11,15,17,21,23,27,29,39,41,45,47,51,53,57,59,69,71,75,77,

%T 81,83,87,89,99,101,105,107,111,113,117,119,129,131,135,137,141,143,

%U 147,149,159,161,165,167,171,173,177,179,189,191,195,197,201,203,207,209,249,251,255,257,261,263,267,269,279,281,285

%N a(1) = 0, and, for n >= 2, numbers n whose primorial base expansion doesn't contain any nonleading zeros.

%C After the initial zero, numbers n for which A276086(n) produces an even number with no gaps in its prime factorization.

%C Numbers n such that A276086(n) is in A055932; numbers for which A328475(n) is equal to A328572(n) = A003557(A276086(n)).

%C The number of positive terms below prime(m)# = A002110(m) is Sum_{k=1..m} A005867(k). - _Amiram Eldar_, Feb 16 2021

%H Antti Karttunen, <a href="/A328574/b328574.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%t max = 4; bases = Prime @ Range[max, 1, -1]; nmax = Times @@ bases - 1; Join[{0}, Select[Range[nmax], FreeQ[IntegerDigits[#, MixedRadix[bases]], 0] &]] (* _Amiram Eldar_, Feb 16 2021 *)

%o (PARI)

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o isA055932(n) = { my(f=factor(n)[, 1]~); f==primes(#f); }; \\ From A055932

%o isA328574(n) = isA055932(A276086(n));

%o (PARI)

%o A328475(n) = { my(m=1, p=2, y=1); while(n, if(n%p, m *= p^((n%p)-y), y=0); n = n\p; p = nextprime(1+p)); (m); };

%o A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };

%o isA328574(n) = (A328475(n) == A328572(n));

%Y Cf. A002110, A003557, A005867, A055932, A276086, A328475, A328572.

%Y Positions of 1's in A328573, positions of 0's in A329027, cf. also A328840.

%Y Cf. A227157 for analogous sequence.

%K nonn,base

%O 1,3

%A _Antti Karttunen_, Oct 20 2019

%E Primary definition changed, the old definition moved to comment section by _Antti Karttunen_, Nov 03 2019

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)