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A060276 a(1) = 2; a(n) = smallest prime > a(n-1) such that the sum of any three nondecreasing terms, chosen from a(1), ..., a(n-1) and a(n), is unique. 1
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; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

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.

PROG

(PARI) {unique(v)=local(b); b=1; for(j=2, length(v), if(v[j-1]==v[j], b=0)); b}

{news(v, q)=local(s); s=[]; for(i=1, length(v), s=concat(s, v[i]+q)); s}

{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))}

CROSSREFS

Cf. A051912.

Sequence in context: A052919 A005807 A167422 * A025563 A224929 A110887

Adjacent sequences:  A060273 A060274 A060275 * A060277 A060278 A060279

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Mar 23 2001

EXTENSIONS

Edited and extended by Klaus Brockhaus, May 16 2003

STATUS

approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)