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Rémy Sigrist, <a href="/A306581/b306581.txt">Table of n, a(n) for n = 1..10000</a>

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Rémy Sigrist: added b-file

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a = {1}; c[x_, y_] := FromDigits[Join @@ IntegerDigits[{x, y}, 2], 2]; While[Length@a < 67, j=1; While[MemberQ[a, j] || ! (PrimeQ@ c[a[[-1]], j] || PrimeQ@ c[j, a[[-1]]]), j++]; AppendTo[a, j]]; a (* Giovanni Resta, Feb 27 2019 *)

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Rémy Sigrist, <a href="/A306581/a306581_4.png">Colored scatterplot of (n, a(n)) for n = 1..10000</a> (where the color corresponds to the parity of a(n): red for odd, blue for even)

Rémy Sigrist, <a href="/A306581/a306581_15.png">ScatterplotColored scatterplot of (n, a(n)-n) for n = 1..1000000</a> (where the color corresponds to the parity of a>(n)-n: red for odd, blue for even)

Rémy Sigrist, <a href="/A306581/a306581_36.png">Colored scatterplotScatterplot of (n, a(n)-n) for n = 1..1000000</a> (where the first color1000000 correspondsterms toof the ordinal paritytransform of n -> a(n)-n: red for odd, blue for even)</a>

Rémy Sigrist, <a href="/A306581/a306581_21.gp.pngtxt">Scatterplot of the first 1000000 terms of the ordinalPARI transformprogram offor n -> a(n)-nA306581</a>

Rémy Sigrist, <a href="/A306581/a306581.gp.txt">PARI program for A306581</a>

The first terms, alongside their binary representations, and the concatenation of consecutive terms, with prime numbers denoted by a star, are:

n a(n) bin(a(n)) bin(a(n)a(n+1)) bin(a(n+1)a(n))

-- ---- --------- --------------- ---------------

1 1 1 110 101*

2 2 10 1011* 1110

3 3 11 11100 10011*

4 4 100 100101* 101100

5 5 101 101110 110101*

6 6 110 1101011* 1011110

7 11 1011 10111000 10001011*

8 8 1000 1000111* 1111000

9 7 111 1111001 1001111*

10 9 1001 10011101* 11011001

1, 2, 3, 4, 5, 6, 711, 8, 117, 9, 13, 10, 1317, 12, 25, 18, 1923, 15, 14, 19, 20, 21, 26, 1727, 1831, 2529, 16, 3337, 2034, 2145, 22, 39, 23, 26, 27, 28, 37, 3055, 2946, 3257, 35, 24, 31, 34, 43, 42, 55, 36, 47, 33, 3832, 41, 48, 4938, 4567, 4630, 5753, 4442, 5161, 40, 63, 5049, 6948, 5273, 6150, 5451, 5359, 56, 5969, 6244, 6563, 6852, 7577, 5860, 79, 54, 65

Rémy Sigrist, <a href="/A306581/a306581_3.png">Colored scatterplot of (n, a(n)-n) for n = 1..1000000</a> (where the color corresponds to the parity of a(n)-n: red for odd, blue for even)

Rémy Sigrist, <a href="/A306581/a306581_3.png">Colored scatterplot of (n, a(n)-n) for n = 1..1000000</a> (where the color corresponds to the parity of a(n)-n: red for odd, blue for even)