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

Author

Naohiro Nomoto, Mar 23 2001

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A051912.

Programs

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
				

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

Extensions

Edited and extended by Klaus Brockhaus, May 16 2003

More terms from Chai Wah Wu, Sep 05 2023