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A365513
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Lexicographically earliest permutation of the nonnegative integers with the property that the successive sizes of the gaps between nonprime terms and the successive sizes of the gaps between nonprime digits show the same pattern.
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0
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, 18, 20, 21, 13, 22, 24, 25, 26, 17, 27, 19, 28, 30, 23, 29, 31, 37, 32, 41, 43, 47, 33, 34, 53, 59, 61, 35, 36, 67, 38, 71, 39, 73, 79, 83, 40, 89, 42, 97, 101, 103, 107, 44, 45, 46, 109, 48
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OFFSET
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1,3
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COMMENTS
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The nonprime integers and the prime numbers appear in their natural order.
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LINKS
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EXAMPLE
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Sequence read as a succession of terms:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, ...
The gaps between nonprime terms are of size:
0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
Sequence read as a succession of digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 1, 4, 1, 1, 1, 5, 1, 6, ...
The gaps between nonprime digits are of size:
0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
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MATHEMATICA
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a[1]=0; a[n_]:=a[n]=(k=1; While[MemberQ[s=Array[a, n-1], k]||PrimeQ@k!= PrimeQ[Flatten[IntegerDigits/@Join[s, {k}]][[n]]], k++]; k); Array[a, 70] (* Giorgos Kalogeropoulos, Sep 07 2023 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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