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

10, 15, 10, 49, 121, 143, 187, 551, 23, 319, 31, 407, 41, 301, 235, 159, 59, 1891, 1943, 71, 803, 395, 83, 2759, 97, 1717, 3193, 749, 109, 565, 3175, 131, 2329, 1807, 7301, 6493, 471, 1793, 1169, 173, 1611, 5611, 2101, 3281, 985, 199, 211, 223, 1135, 4351, 5359, 11233, 2651

Offset: 1

Author

Zak Seidov, Jul 04 2017

Keywords

• nonn

Comments

Are all terms distinct? Is a(1)=a(3)=10 the only case of equality?

Examples

			a(1)=10=A034961(1), a(2)=15=A034961(2), a(3)=319=A034961(27).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Zak Seidov, Graph of first 50 terms.

Crossrefs

Cf. A034961, A034962 (subsequence).

Programs

Mathematica

Table[Function[p, k = 1; While[! Divisible[Set[s, Total@ Prime@ Range[k, k + 2]], p], k++]; s]@ Prime@ n, {n, 53}] (* or *)
s = Total /@ Partition[Prime@ Range[10^4], 3, 1]; Table[SelectFirst[s, Divisible[#, Prime@ n] &], {n, 53}] (* Michael De Vlieger, Jul 04 2017 *)

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

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)
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