

A271564


Number of 6's found in the first differences of a reduced residue system modulo a primorial p#.


2



0, 0, 2, 14, 142, 1690, 26630, 470630, 10169950, 280323050, 8278462850, 293920842950, 11604850743850, 481192519512250, 21869408938627250, 1124832660535333750, 64590101883781223750, 3837395864206055401250, 250972362651045466681250, 17415757437491856599406250, 1243227958252662737649043750
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OFFSET

1,3


COMMENTS

Technically, the formula is undefined modulo 2# or 3#, but their values are listed as "0", since there are no 6's in the first differences of their reduced residue systems. For our purposes, by "6's", we mean n such that n,n+6 are relatively prime to the primorial modulus, while n+1,n+2,n+3,n+4,n+5 all share a factor (or factors) with p#. The values of this sequence are tied to actual distribution of sexy primes over N (conjecture).


LINKS

Table of n, a(n) for n=1..21.


FORMULA

a(n) = 2*product(p2)2*product(p3), where p runs over the primes greater than 3.


EXAMPLE

Modulo 5# (=30), there are (2*(52)2*(53))=2 occurrences where n,n+6 are relatively prime, but n+1,n+2,n+3,n+4,n+5 share a factor with 30; they are n=1,n=23(mod30). Modulo 7# (=210), there are (2*(72)*(52)2*(73)*(53))=3016=14 such occurrences.


MATHEMATICA

Table[2 Product[Prime@ k  2, {k, 3, n}]  2 Product[Prime@ k  3, {k, 3, n}], {n, 21}] (* Michael De Vlieger, Apr 11 2016 *)


PROG

(PARI) a(n) = 2*prod(k=3, n, prime(k)2)  2*prod(k=3, n, prime(k)3); \\ Michel Marcus, Apr 10 2016


CROSSREFS

Cf. A059861 (d=2,4 values), A049296, A271565.
Sequence in context: A111424 A224729 A245267 * A100510 A087132 A036079
Adjacent sequences: A271561 A271562 A271563 * A271565 A271566 A271567


KEYWORD

nonn,easy


AUTHOR

Logan W. Wilbur, Apr 09 2016


EXTENSIONS

Corrected and extended by Michel Marcus, Apr 10 2016


STATUS

approved



