

A271565


Number of 8's found in the first differences of a reduced residue system modulo a primorial p#.


2



0, 0, 0, 2, 28, 394, 6812, 128810, 2918020, 83120450, 2524575200, 91589444450, 3682730287600, 155231331960250, 7156139793803000, 372520258834974250, 21613446896458917500, 1296556574981939521250, 85520460088068245240000, 5980843188551617897761250, 430093937447553491544932500
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OFFSET

1,4


COMMENTS

Technically, the formula is undefined modulo 2# or 3#, but I have listed their values as "0", since there are no 8's in the first differences of their reduced residue systems. For our purposes, by "8's", we mean n such that n,n+8 are relatively prime to the primorial modulus, while n+1,n+2,n+3,n+4,n+5,n+6,n+7 all share a factor (or factors) with p#.


LINKS

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


FORMULA

a(n) = product(p2)  2*product(p3) + product(p4), where p runs through the primes > 3 and <= prime(n).


EXAMPLE

Modulo 5# (=30), there are (52)2*(53)+(54)=0 occurrences where n, n+8 are relatively prime but n+1, n+2, n+3, n+4, n+5, n+6, n+7 share a factor with 30.
Modulo 7# (=210), there are (72)(52)2*(73)(53)+(74)(54)=1516+3=2 such occurrences; i.e when n=89,113 (mod210).


MATHEMATICA

Table[Product[Prime@ k  2, {k, 3, n}]  2 Product[Prime@ k  3, {k, 3, n}] + Product[Prime@ k  4, {k, 3, n}], {n, 21}] (* Michael De Vlieger, Apr 11 2016 *)


PROG

(PARI) a(n) = prod(k=3, n, prime(k)2)  2*prod(k=3, n, prime(k)3) + prod(k=3, n, prime(k)4); \\ Michel Marcus, Apr 11 2016


CROSSREFS

Cf. A049296, A059861, A271564.
Sequence in context: A061629 A230130 A011944 * A241365 A240771 A012745
Adjacent sequences: A271562 A271563 A271564 * A271566 A271567 A271568


KEYWORD

nonn,easy


AUTHOR

Logan W. Wilbur, Apr 10 2016


EXTENSIONS

More terms from Michel Marcus, Apr 11 2016


STATUS

approved



