A328762 - OEIS

A328762

Numbers n for which 2 < A257993(A276086(A276086(n))) < A257993(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.

210, 1470, 5250, 6510, 7140, 8400, 9450, 10710, 14490, 15750, 16380, 17640, 18690, 19950, 23730, 24990, 25620, 26880, 27930, 29190, 30030, 31290, 32340, 33600, 37380, 38640, 39270, 40530, 41580, 42840, 46620, 47880, 48510, 49770, 50820, 52080, 55860, 57120, 57750, 59010, 60270, 61530, 63420, 65730, 69510, 70770, 72660, 74970

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OFFSET

1,1

COMMENTS

All terms are multiples of 5 (and thus of 30), because when applied to any number which is a multiple of 6, but not of 5 (and thus not a multiple of 30, implying that the primorial expansion ends with "x00", where x <> 0, and A257993(n) = 3), A276086 will yield a number of the form 30k+5 or 30k+25 (A084967) whose primorial expansion ends either as "...021" or as "...401" (with the least significant zero either in position 2 or 3), thus A328578(n) = A257993(A276086(A276086(n))) cannot simultaneously be larger than 2 and smaller than A257993(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

PROG

(PARI)

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

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

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

isA328762(n) = { my(u=A328578(n)); ((u > 2) && (u < A257993(n))); };

CROSSREFS

Setwise difference A328587 \ A328632.

Cf. A257993, A276086, A328578, A328589.