This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)