A247245 -id:A247245 - cp's OEIS frontend

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

Zak Seidov, Jan 06 2012

nonn

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

			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.

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

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

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

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 *)

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

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

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

A247252 Smallest integer k>=1 such that k*prime(n) is the sum of two successive primes.

Original entry on oeis.org

4, 4, 1, 6, 18, 4, 4, 8, 6, 24, 6, 6, 10, 4, 12, 24, 8, 20, 4, 12, 20, 28, 18, 8, 12, 18, 6, 12, 8, 22, 4, 6, 4, 12, 8, 6, 24, 6, 4, 36, 18, 36, 20, 4, 24, 20, 30, 4, 24, 6, 16, 52, 6, 18, 6, 30, 42, 18, 30, 24, 4, 6, 24, 6, 6, 8, 8, 6, 12, 12, 24, 8, 26, 12, 10, 16, 6, 12, 8, 42, 14, 10, 18, 6, 8, 12, 30, 36, 48, 22, 12, 14, 4, 12, 20, 16, 6, 6, 6, 20

Offset: 1

Zak Seidov, Nov 29 2014

nonn

Except for a(3)=1, all terms are even and >= 4.

			If n=1, prime(1)=2, and 4*2 = 8 = 3+5 is the sum of two consecutive primes, thus a(1) = 4.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A000040, A001043, A203836, A247245.

a(n) = A203836(n)/prime(n).

A260966 a(0)=1, then a(n) is the least sum of two successive primes that is a multiple of n and > a(n-1).

Original entry on oeis.org

1, 5, 8, 12, 24, 30, 36, 42, 112, 144, 210, 308, 360, 390, 434, 450, 480, 918, 990, 1064, 1120, 1428, 1518, 1656, 1848, 1900, 2132, 2430, 2604, 2610, 2640, 2728, 2912, 2970, 2992, 3010, 3240, 3330, 3952, 4056, 4680, 5740, 6090, 6450, 6600, 6660, 6762, 7990, 8256, 8428, 9000, 9282, 9308

Offset: 0

Zak Seidov, Aug 06 2015

nonn

			a(1)=5=2+3, a(2)=8=3+5, a(3)=12=5+7, a(4)=24=11+13, a(5)=30=13+17.

Robert Israel, Table of n, a(n) for n = 0..4628

Cf. A001043, A247245.

N:= 10^5: # get all terms using primes <= N
Primes:= select(isprime,[2,(2*i+1 $ i=1..floor((N-1)/2))]):
Sprimes:= Primes[1..-2] + Primes[2..-1]:
A[0]:= 1: x[0]:= 0: ok:= true:
for n from 1 while ok do
  ok:= false;
  for t from x[n-1]+1 to nops(Sprimes) do
    if Sprimes[t] mod n = 0 then
      A[n]:= Sprimes[t]; x[n]:= t; ok:= true; break
    fi
  od
od:
seq(A[i],i=0..n-2); # Robert Israel, Aug 06 2015

Prepend[Reap[n=1;Do[If[Mod[(a=Prime[k]+Prime[k+1]),n]<1,Sow[a];i++],{k,1000}]][[2,1]],1]
nxt[{n_,a_}]:=Module[{sprs=Total/@Partition[Prime[Range[1000]],2,1]},{n+1, SelectFirst[sprs,Divisible[#,n+1]&&#>a&]}]; Transpose[ NestList[ nxt,{0,1},60]][[2]] (* Harvey P. Dale, Jun 02 2016 *)

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

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A247252 Smallest integer k>=1 such that k*prime(n) is the sum of two successive primes.

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A260966 a(0)=1, then a(n) is the least sum of two successive primes that is a multiple of n and > a(n-1).

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