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A096023
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Numbers congruent to {63, 123, 183, 243, 303, 363} mod 420.
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5
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63, 123, 183, 243, 303, 363, 483, 543, 603, 663, 723, 783, 903, 963, 1023, 1083, 1143, 1203, 1323, 1383, 1443, 1503, 1563, 1623, 1743, 1803, 1863, 1923, 1983, 2043, 2163, 2223, 2283, 2343, 2403, 2463, 2583, 2643, 2703, 2763, 2823, 2883, 3003, 3063, 3123
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 4 and (n+5) mod 7 <> 1.
Numbers n such that n mod 60 = 3 and n mod 420 <> 3.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).
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FORMULA
| G.f. 3*x*(21+20*x+20*x^2+20*x^3+20*x^4+20*x^5+19*x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
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EXAMPLE
| 63 mod 2 = 64 mod 3 = 65 mod 4 = 66 mod 5 = 67 mod 6 = 1 and 68 mod 7 = 5, hence 63 is in the sequence.
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PROG
| (PARI) {k=5; m=3150; for(n=1, m, j=0; b=1; while(b&&j<k, if((n+j)%(2+j)==1, j++, b=0)); if(b&&(n+k)%(2+k)!=1, print1(n, ", ")))}
(MAGMA) [ n : n in [1..3500] | n mod 420 in [63, 123, 183, 243, 303, 363] ]. - Vincenzo Librandi, Mar 24 2011
(MAGMA) Alternatively: &cat[ [ 60*n+3, 60*n+63 ]: n in [1..52] | n mod 7 in [1, 3, 5] ]; // Bruno Berselli, Mar 25 2011
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CROSSREFS
| Cf. A007310, A017629, A096022, A096024, A096025, A096026, A096027.
Cf. A047391 (see Magma code) - Bruno Berselli, Mar 25 2011
Sequence in context: A038851 A038865 A181556 * A080947 A023720 A031468
Adjacent sequences: A096020 A096021 A096022 * A096024 A096025 A096026
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 15 2004
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EXTENSIONS
| New definition from Ralf Stephan, Dec 01, 2004
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