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A096022
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Numbers congruent to {15, 27, 39, 51} mod 60.
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6
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15, 27, 39, 51, 75, 87, 99, 111, 135, 147, 159, 171, 195, 207, 219, 231, 255, 267, 279, 291, 315, 327, 339, 351, 375, 387, 399, 411, 435, 447, 459, 471, 495, 507, 519, 531, 555, 567, 579, 591, 615, 627, 639, 651, 675, 687, 699, 711, 735, 747, 759, 771, 795
(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 2 and (n+3) mod 5 <> 1.
This is one of a family of sequences which are defined (or could be defined) according to the same scheme: Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to k-1 and (n+k) mod (2+k) <> 1. We have A007310 for k = 1, A017629 for k = 2, this one (A096022) for k = 3, A096023 for k = 5, A096024 for k = 6, A096025 for k = 7, A096026 for k = 9, A096027 for k = 11. Remarkably these sequences are empty for k = 4, 8, 10, ... (i.e. if k+1 is a term of A080765).
Numbers n such that n mod 12 = 3 and n mod 60 <> 3.
Subsequence of A017557: 12n+3.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
| G.f. 3*x*(5+4*x+4*x^2+4*x^3+3*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
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EXAMPLE
| 51 mod 2 = 52 mod 3 = 53 mod 4 = 1 and 54 mod 5 = 4, hence 51 is in the sequence; 3 mod 2 = 4 mod 3 = 5 mod 4 = 6 mod 5 = 1, hence 3 is not in the sequence.
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PROG
| (PARI) {k=3; m=800; 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..1500] | n mod 60 in [15, 27, 39, 51] ]. - Vincenzo Librandi, Mar 24 2011
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CROSSREFS
| Cf. A017557, A007310, A017629, A080765, A096023, A096024, A096025, A096026, A096027.
Sequence in context: A091236 A053177 A145195 * A097222 A004069 A110978
Adjacent sequences: A096019 A096020 A096021 * A096023 A096024 A096025
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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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