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Search: id:A060276
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| A060276 |
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a(1) = 2; a(n) = smallest prime > a(n-1) such that the sum of any three non-decreasing terms, chosen from a(1), ..., a(n-1) and a(n), is unique. |
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2
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| 2, 3, 7, 19, 59, 73, 211, 257, 631, 919, 1291, 1979, 3229, 4397, 5557, 7151, 10657, 12049, 17827, 19577, 25919, 32143, 35951, 46141, 54499, 64433, 81199, 92507, 116009, 132511, 145303, 171763, 193679, 232417, 260549, 289573, 302009
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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For {2,3,5} the sums are not unique: 2+2+5 = 3+3+3. Three terms chosen from {2,3,7} can be 2+2+2; 2+2+3; 2+3+3; 3+3+3; 2+2+7; 2+3+7; 3+3+7; 2+7+7; 3+7+7; 7+7+7; the sums are all distinct,
so a(3) = 7.
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PROGRAM
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(PARI) {unique(v)=local(b); b=1; for(j=2, length(v), if(v[j-1]==v[j], b=0)); b}
(PARI) {news(v, q)=local(s); s=[]; for(i=1, length(v), s=concat(s, v[i]+q)); s}
(PARI) {m=310000; print1(p=2, ", "); w1=[p]; w2=[p+p]; w3=[p+p+p]; q=nextprime(p+1); while(q<m, y1=concat(w1, q); y2=concat(w2, news(y1, q)); y3=vecsort(concat(w3, news(y2, q))); if(unique(y3), w1=y1; w2=y2; w3=y3; print1(q, ", ")); q=nextprime(q+1))}
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CROSSREFS
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Cf. A051912.
Sequence in context: A037028 A052919 A005807 this_sequence A025563 A110887 A065060
Adjacent sequences: A060273 A060274 A060275 this_sequence A060277 A060278 A060279
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KEYWORD
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nonn
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AUTHOR
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Naohiro Nomoto (6284968128(AT)geocities.co.jp), Mar 23 2001
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 16 2003
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