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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 (list; graph; refs; listen; history; text; internal format)
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(p-2)-2*product(p-3), where p runs over the primes greater than 3.

EXAMPLE

Modulo 5# (=30), there are (2*(5-2)-2*(5-3))=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*(7-2)*(5-2)-2*(7-3)*(5-3))=30-16=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: A303395 A301271 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

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Last modified October 22 08:43 EDT 2018. Contains 316432 sequences. (Running on oeis4.)