A326810 - OEIS

%I #25 Oct 22 2019 21:26:51

%S 2,3,2,5,2,5,2,3,2,7,2,7,2,3,2,7,2,7,2,3,2,7,2,7,2,3,2,7,2,7,2,3,2,5,

%T 2,5,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,5,

%U 2,5,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,11,2,11,2,3,2,5,2,5,2,3,2,11,2,11,2,3,2,11

%N The smallest prime that does not divide the prime product form (A276086) of the primorial base expansion of n.

%H Antti Karttunen, <a href="/A326810/b326810.txt">Table of n, a(n) for n = 0..32768</a>

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

%F a(n) = A053669(A276086(n)).

%F a(n) = A000040(A328570(n)).

%F a(n) = A020639(A276087(n)) = A020639(A328613(n)).

%F a(n) = A276087(n) / A276086(A328476(n)).

%F For all odd n, a(n) > A276088(n).

%F For all n >= 0, a(A276086(n)) = A328579(n).

%F For all n >= 1, A328317(n) = a(A328316(n-1)).

%t With[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Table[Block[{p = 2}, While[Mod[#, p] == 0, p = NextPrime@ p]; p] &@ Apply[Times, Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #}] &@ IntegerDigits[n, b], {n, 0, 105}]] (* _Michael De Vlieger_, Oct 22 2019 *)

%o (PARI) A326810(n) = { my(i=1, p=2); while(n && (n%p), n = n\p; p = nextprime(1+p)); (p); };

%Y Cf. A053669, A143293, A276086, A276087, A276088, A328476, A328570, A328579, A328580.

%Y Cf. also A328316, A328317, A328613.

%K nonn

%O 0,1

%A _Antti Karttunen_, Oct 19 2019