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A129198
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Slater-Velez permutation sequence of the 2nd kind.
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2
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1, 2, 5, 3, 11, 7, 23, 4, 47, 42, 95, 89, 191, 6, 383, 376, 767, 8, 1535, 1526, 3071, 9, 6143, 6133, 12287, 10, 24575, 24564, 49151, 49139, 98303, 12, 196607, 196594, 393215, 13, 786431, 786417, 1572863, 14, 3145727, 3145712, 6291455, 15, 12582911
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is known to be a permutation of positive integers, along with its absolute difference sequence (A129199).
The rule for constructing the sequence is as follows: a(1)=1, a(2)=2, then apply the following recursion, assuming the members are already present up to index k: let M(k)=max(a(1),a(2),...,a(k)) and let n(k) be the smallest positive integer not present in the sequence yet, while m(k) the smallest integer not present in the absolute difference sequence (d(1),d(2),...,d(k-1)), so far. Then a(k+1)=2M(k)+1 and if m(k)<=n(k) then set a(k+2)=a(k+1)-m(k), else a(k+2)=n(k).
In the paper of Slater and Velez it is shown that both the sequence a(n) and d(n) are permutations of positive integers (in spite of their strange appearance).
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LINKS
| P. J. Slater and W. Y. Velez, Permutations of the Positive Integers with Restrictions on the Sequence of Differences, Pacific J. Math., 71, 1977
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PROG
| (PARI) {SV_p2(n)=local(x, v=6, d=2, j, k, mx=2, nx=3, nd=2, u, w); /* Slater-Velez permutation - the 2nd kind */ x=vector(n); x[1]=1; x[2]=2; forstep(i=3, n, 2, k=x[i]=2*mx+1; if(nd<=nx, j=x[i]-nd, j=nx); x[i+1]=j; mx=max(mx, max(j, k)); v+=2^k+2^j; u=abs(k-x[i-1]); w=abs(j-k); d+=2^u+2^w; print(i" "k" "j" "u" "w); while(bittest(v, nx), nx++); while(bittest(d, nd), nd++)); return(x)}
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CROSSREFS
| The absolute difference is in A129199, Cf. A081145, which can be called as Slater-Velez permutation sequence of the first kind.
Sequence in context: A178174 A094744 A185061 * A122442 A162613 A120858
Adjacent sequences: A129195 A129196 A129197 * A129199 A129200 A129201
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KEYWORD
| nonn
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AUTHOR
| Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), Apr 04 2007
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