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 A059865 Product_{i=4..n} (prime(i) - 6). 6
 1, 1, 1, 1, 5, 35, 385, 5005, 85085, 1956955, 48923875, 1516640125, 53082404375, 1964048961875, 80526007436875, 3784722349533125, 200590284525255625, 11032465648889059375, 672980404582232621875, 43743726297845120421875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Arises in Hardy-Littlewood prime k-tuplet conjectural formulas. Also the sequence gives the exact numbers of X42424Y difference-pattern in dRRS[m], where m=modulus=A002110(n). See A049296 (=dRRS[210]=list of first differences of reduced residue system modulo 210=4th primorial). A pattern X42424Y corresponds to a residue-sextuple or it is their difference-quintuple, X,Y > 4. Analogous pattern for primes is in A022008. a(352) has 1001 decimal digits. - Michael De Vlieger, Mar 06 2017 REFERENCES See A059862 for references. Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..351 C. K. Caldwell, Prime k-tuple Conjecture Steven R. Finch, Hardy-Littlewood Constants [Broken link] Steven R. Finch, Hardy-Littlewood Constants [From the Wayback machine] G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy] EXAMPLE a(7) = (prime(4)-6) * (prime(5)-6) * (prime(6)-6) * (prime(7)-6) = 1 * 5* 7 *11 = 385 Also in one period of dRRS with 2,6,30,210,2310,... modulus [A002110(n)] 1,2,8,48,480,... differences occur [A005867(n)]. The number of X42424Y residue-difference-patterns are 0,1,1,1,5,... respectively starting at suitable residues coprime to A002110(n). MATHEMATICA Table[Product[Prime@ i - 6, {i, 4, n}], {n, 19}] (* Michael De Vlieger, Mar 06 2017 *) PROG (PARI) a(n) = prod(k=4, n, prime(k) - 6); \\ Michel Marcus, Mar 06 2017 CROSSREFS Cf. A049296, A002110, A005867, A000847, A022008, A051160-A051168, A048298, A059861-A059865. Sequence in context: A125864 A210996 A204290 * A247596 A325408 A097492 Adjacent sequences:  A059862 A059863 A059864 * A059866 A059867 A059868 KEYWORD nonn AUTHOR Labos Elemer, Feb 28 2001 STATUS approved

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Last modified September 16 06:21 EDT 2019. Contains 327090 sequences. (Running on oeis4.)