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A289361 Least sum s of three consecutive primes such that s is a multiple of the n-th prime.

%I A289361 #24 May 25 2020 05:47:53
%S A289361 10,15,10,49,121,143,187,551,23,319,31,407,41,301,235,159,59,1891,
%T A289361 1943,71,803,395,83,2759,97,1717,3193,749,109,565,3175,131,2329,1807,
%U A289361 7301,6493,471,1793,1169,173,1611,5611,2101,3281,985,199,211,223,1135,4351,5359,11233,2651
%N A289361 Least sum s of three consecutive primes such that s is a multiple of the n-th prime.
%C A289361 Are all terms distinct? Is a(1)=a(3)=10 the only case of equality?
%H A289361 Charles R Greathouse IV, <a href="/A289361/b289361.txt">Table of n, a(n) for n = 1..10000</a>
%H A289361 Zak Seidov, <a href="/A289361/a289361_1.png">Graph of first 50 terms.</a>
%e A289361 a(1)=10=A034961(1), a(2)=15=A034961(2), a(3)=319=A034961(27).
%t A289361 Table[Function[p, k = 1; While[! Divisible[Set[s, Total@ Prime@ Range[k, k + 2]], p], k++]; s]@ Prime@ n, {n, 53}] (* or *)
%t A289361 s = Total /@ Partition[Prime@ Range[10^4], 3, 1]; Table[SelectFirst[s, Divisible[#, Prime@ n] &], {n, 53}] (* _Michael De Vlieger_, Jul 04 2017 *)
%o A289361 (PARI) a(n)=p = 2; q = 3; pn = prime(n); forprime(r=5,,if (((s=p+q+r) % pn) == 0, return (s)); p = q; q = r;); \\ _Michel Marcus_, Jul 04 2017
%o A289361 (PARI) isA034961(n)=my(p=precprime(n\3),q=nextprime(n\3+1),r=n-p-q); if(r>q, r==nextprime(q+2), r==precprime(p-1) && r)
%o A289361 a(n,p=prime(n))=if(p==5, return(10)); my(k=1); while(!isA034961(p*k), k+=2); p*k \\ _Charles R Greathouse IV_, Jul 05 2017
%Y A289361 Cf. A034961, A034962 (subsequence).
%K A289361 nonn
%O A289361 1,1
%A A289361 _Zak Seidov_, Jul 04 2017