A326810 The smallest prime that does not divide the prime product form (A276086) of the primorial base expansion of n.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Oct 19 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

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

Cf. also A328316, A328317, A328613.

Programs

Mathematica

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 *)

PARI

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

Formula

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

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

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

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

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

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

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