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A254897
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Define a family of sequences as follows: a(1) and a(2) are prime numbers, then if a(n-2) and a(n-1) have the same parity a(n)=(a(n-2)+a(n-1))/2 and if not a(n)=a(n-2)/2+a(n-1) for a(n-2) even or a(n)=a(n-2)+a(n-1)/2 for a(n-1) even. Start the first sequence with the two smallest prime numbers 2 and 3; in general, start the next sequence with the two smallest prime numbers not present in all preceding sequences; the present sequence lists the initial term of all these sequences.
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1
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2, 19, 31, 59, 83, 107, 113, 149, 157, 181, 197, 229, 241, 263, 271, 307, 313, 331, 353, 367, 379, 389, 409, 431, 439, 457, 487, 499, 541, 569, 577, 593, 601, 617, 647, 661, 719, 733, 751, 809, 823, 853, 859, 877, 883, 911, 937, 953, 977, 997, 1019
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1)=2, the first term of the sequence A254498.
a(2)=19, the first term of the sequence A254330.
a(3)=31, the smallest prime number not present in A254498 and A254330, and the next one is 37, 31 and 37 starts the third sequence define by the rule, and so on.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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