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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 (list; graph; refs; listen; history; text; internal format)
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(p-2) - 2*product(p-3) + product(p-4), where p runs through the primes > 3 and <= prime(n).

EXAMPLE

Modulo 5# (=30), there are (5-2)-2*(5-3)+(5-4)=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 (7-2)(5-2)-2*(7-3)(5-3)+(7-4)(5-4)=15-16+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

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Last modified February 19 09:07 EST 2018. Contains 299330 sequences. (Running on oeis4.)