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.

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, 340111, 424967, 465151, 506507

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..194

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))}
(Python)
from itertools import count, islice
from sympy import nextprime
def A060276_gen(): # generator of terms
    aset1, aset2, aset3, alist, k = set(), set(), set(), [], 2
    while True:
        bset2, bset3 = {k<<1}, {3*k}
        if 3*k not in aset3:
            for d in aset1:
                if (m:=d+(k<<1)) in aset3:
                    break
                bset2.add(d+k)
                bset3.add(m)
            else:
                for d in aset2:
                    if (m:=d+k) in aset3:
                        break
                    bset3.add(m)
                else:
                    yield k
                    alist.append(k)
                    aset1.add(k)
                    aset2.update(bset2)
                    aset3.update(bset3)
        k = nextprime(k)
A060276_list = list(islice(A060276_gen(), 40)) # Chai Wah Wu, Sep 05 2023

Crossrefs

Cf. A051912.

Sequence in context: A052919 A005807 A167422 * A337187 A358049 A025563

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

More terms from Chai Wah Wu, Sep 05 2023

Status

approved