cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Zak Seidov, Jan 06 2012

Keywords

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

  • 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 *)
  • 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

Formula

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