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A236269
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First differences of Stanley sequence S(0,4) (A005487).
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3
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4, 1, 2, 4, 1, 4, 7, 3, 5, 2, 4, 1, 6, 5, 7, 17, 5, 2, 5, 10, 4, 7, 18, 4, 3, 5, 7, 26, 19, 9, 6, 17, 1, 5, 1, 11, 9, 12, 10, 7, 8, 3, 15, 6, 2, 3, 6, 18, 48, 7, 5, 25, 12, 21, 11, 4, 21, 2, 6, 5, 50, 5, 21, 18, 30, 1, 6, 5, 4, 6, 4, 1, 2, 20, 10, 4, 24, 3, 13, 5
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OFFSET
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1,1
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COMMENTS
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Also first differences of Stanley sequence S(1,5) (A033158).
While there are conjectures about formulas for S(0,m), m=1,2,3,6,9... (see A093682), m=4 is the first case where the first differences look almost random.
Records are 4, 7, 17, 18, 26, 48, 50, 55, 76, 87, 92, 93, 165, 175,...
Positions of records are 1, 7, 16, 23, 28, 49, 61, 81, 83, 101, 147, 165, 185, 250, 400,...
Positions where a(n)=1: 2, 5, 12, 33, 35, 66, 72, 94, 125, 160, 189, 288, 307, 327,...
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LINKS
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Ralf Stephan, Table of n, a(n) for n = 1..4650
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PROG
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(PARI) NAP(sv, N)=local(v, vv, m, k, l, sl, vvl); sl=length(sv); vvl=min(N*N, 10^5); v=vector(N); vv=vector(vvl); for(k=1, sl, v[k]=sv[k]; for(l=1, k-1, vv[2*v[k]-v[l]]=1)); m=v[sl]+1; for(k=sl+1, N, while(m<=vvl&&vv[m], m=m+1); if(m>vvl, return(v)); for(l=1, k-1, sl=2*m-v[l]; if(sl<=vvl, vv[sl]=1)); vv[m]=1; v[k]=m); v
S04(n)=N=1000; NAP([0, 4], N)[n]
a(n)=S04(n+1)-S04(n)
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CROSSREFS
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Sequence in context: A080508 A178141 A063987 * A010126 A021712 A307550
Adjacent sequences: A236266 A236267 A236268 * A236270 A236271 A236272
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jan 21 2014
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STATUS
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approved
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