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A109653
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Sequence and first differences include all prime numbers exactly once.
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1
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2, 5, 12, 23, 36, 53, 72, 101, 132, 169, 210, 253, 300, 359, 420, 487, 558, 631, 710, 793, 882, 979, 1082, 1189, 1298, 1411, 1538, 1669, 1806, 1945, 2094, 2245, 2402, 2565, 2732, 2905, 3084, 3265, 3456, 3649, 3846, 4045, 4256, 4479, 4706, 4935, 5168, 5407
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OFFSET
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2,1
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COMMENTS
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Sequence and first differences:
2 5 12 23 36 53 72 101 132 169 210 253 300 359 420...
.3.7.11.13.17.19.29...31..37..41..43..47..59..61...
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LINKS
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EXAMPLE
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All prime numbers appear once and only once, either in the sequence itself or in the first differences.
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {1}; d = 3; k = 2; Do[ While[ Position[a, d] != {}, d += 2 ]; k = k + d; d = NextPrim[d]; a = Append[a, k], {n, 47} ]; a (* Robert G. Wilson v *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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