A203836 Smallest sum s of two consecutive primes such that s = 0 mod prime(n).

8, 12, 5, 42, 198, 52, 68, 152, 138, 696, 186, 222, 410, 172, 564, 1272, 472, 1220, 268, 852, 1460, 2212, 1494, 712, 1164, 1818, 618, 1284, 872, 2486, 508, 786, 548, 1668, 1192, 906, 3768, 978, 668, 6228, 3222, 6516, 3820, 772, 4728, 3980, 6330, 892, 5448, 1374

Offset

1,1

Comments

Besides a(3)=5, all terms are even and >=4. - Zak Seidov, Nov 29 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = 4*prime(n) if prime(n) is in A118134. - Robert Israel, May 25 2020

Example

a(1) = 8 = 3 + 5 is the least sum of two consecutive primes that is a multiple of prime(1) = 2.
a(3) = 5 = 2 + 3 is the least sum of two consecutive primes that is a multiple of prime(3) = 5.

Maple

N := 100: # for a(1)..a(N)
M := ithprime(N):
V := Vector(M):
count:= 0:
for i from 1 while count < N do
  x:= ithprime(i)+ithprime(i+1);
  Q:= convert(select(t -> t <= M and V[t]=0, numtheory:-factorset(x)), list);
  V[Q]:= x;
  count:= count + nops(Q);
od:
seq(V[ithprime(i)], i=1..N); # Robert Israel, May 25 2020

Mathematica

pr=Prime[Range[1000]]; rm=Rest[pr]+Most[pr]; Table[Select[rm, Mod[#, pr[[n]]]==0&][[1]], {n, 50}]
s = Total /@ Partition[Prime@ Range[10^4], 2, 1]; Table[SelectFirst[s, Divisible[#, Prime@ n] &], {n, 52}] (* Michael De Vlieger, Jul 04 2017 *)

Prog

(PARI) a(n)=p = 2; pn = prime(n); forprime(q=3, , if (((s=p+q) % pn) == 0, return (s)); p = q; ); \\ Michel Marcus, Jul 04 2017
(PARI) isA001043(n)=precprime((n-1)/2)+nextprime(n/2)==n&&n>2
a(n, p=prime(n))=if(p==5, return(5)); my(k=2); while(!isA001043(k*p), k+=2); k*p \\ Charles R Greathouse IV, Jul 05 2017

Crossrefs

Cf. A001043, A062703, A111163, A247245, A247252, A188815 (the smaller prime), A118134.

Sequence in context: A173457 A033198 A072900 * A220665 A166173 A014453

Adjacent sequences: A203833 A203834 A203835 * A203837 A203838 A203839

Keyword

nonn

Author

Zak Seidov, Jan 06 2012

Status

approved