A328233 Numbers n such that the arithmetic derivative of A276086(n) is prime.

3, 7, 9, 33, 37, 38, 211, 213, 218, 241, 242, 246, 247, 249, 2313, 2317, 2319, 2341, 2342, 2346, 2521, 2523, 2526, 2529, 2550, 2553, 2559, 30031, 30038, 30039, 30061, 30062, 30063, 30066, 30069, 30242, 30243, 30249, 30270, 30278, 30279, 32341, 32342, 32347, 32370, 32373, 32377, 32379, 32551, 32553, 510513, 510518, 510519

Offset

1,1

Comments

Numbers n for which A327860(n) = A003415(A276086(n)) is a prime.

Numbers n such that A276086(n) is in A157037.

Terms come in distinct "batches", where in each batch they are "slightly more" than the nearest primorial (A002110) below. This is explained by the fact that for A276086(n) to be a squarefree (which is the necessary condition for A157037), n's primorial base expansion (A049345) must not contain digits larger than 1. Thus this is a subsequence of A276156.

Numbers n such that A327860(A276086(n)) = A003415(A276087(n)) is a prime [A276087(n) is in A157037] are much rarer: 2, 4, 30, 212, 421, 30045, 510511, 512820, 9729723, ...

For all terms k in this sequence, A327969(k) <= 4, and particularly A327969(k) = 2 when k is a prime. Otherwise, when k is not a prime, but A003415(k) is, A327969(k) = 3, while for other cases (when k is neither prime nor in A157037), we have A327969(k) = 4.

Links

Antti Karttunen, Table of n, a(n) for n = 1..269

Index entries for sequences related to primorial base

Prog

(PARI)
A327860(n) = { my(m=1, i=0, s=0, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), my(e=((n%nextpr)/pr)); m *= (prime(i)^e); s += (e / prime(i)); n-=(n%nextpr)); pr=nextpr); (s*m); };
isA328233(n) = isprime(A327860(n));

Crossrefs

Cf. A002110, A003415, A051674, A157037, A276086, A327860, A327969, A327978, A328232, A328240.

Subsequence of A276156, of A328116, and of A328242.

Sequence in context: A246659 A072087 A328462 * A031161 A031882 A199190

Adjacent sequences: A328230 A328231 A328232 * A328234 A328235 A328236

Keyword

nonn

Author

Antti Karttunen, Oct 09 2019

Status

approved