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

0,1

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base

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)).

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 *)

Prog

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

Crossrefs

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

Cf. also A328316, A328317, A328613.

Sequence in context: A108501 A166226 A263978 * A263726 A328317 A088167

Adjacent sequences: A326807 A326808 A326809 * A326811 A326812 A326813

Keyword

nonn

Author

Antti Karttunen, Oct 19 2019

Status

approved