A328586 - OEIS

%I #12 Oct 27 2019 17:31:23

%S 6,18,36,48,66,78,96,108,126,138,156,168,186,198,222,234,252,264,282,

%T 294,312,324,342,354,372,384,402,414,426,438,456,468,486,498,516,528,

%U 546,558,576,588,606,618,642,654,672,684,702,714,732,744,762,774,792,804,822,834,846,858,876,888,906,918,936,948,966,978,996,1008

%N Even numbers n for which A257993(n) is equal to A257993(A276086(A276086(n))), where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.

%C All terms are multiples of 6, but very few multiples of 5 (and thus of 10) are present: the first ones are at a(169) = 2520 and a(254) = 3780. Among the first 10000 terms, there are only 28 ending with decimal digit 0, while those that end with either 2 or 4 are 2450 both, and with either 6 or 8, both have 2536 each.

%C Other multiples of six are in A328587 and A328589.

%H Antti Karttunen, <a href="/A328586/b328586.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>

%o (PARI)

%o A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }

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

%o A328578(n) = A257993(A276086(A276086(n)));

%o isA328586(n) = ((!(n%2))&&(A328578(n) == A257993(n)));

%Y Cf. A257993, A276086, A328578, A328316, A328317, A328633.

%Y Even terms in A328585. Cf. also A328587, A328588, A328589.

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 21 2019