A352534 First of four consecutive primes p,q,r,s such that p+q+r+s is divisible by A001414(r+s).

5, 11, 13, 97, 101, 109, 277, 293, 389, 653, 739, 863, 1019, 1297, 1319, 1321, 1481, 1759, 1979, 2293, 2557, 2719, 3209, 3511, 3889, 3947, 5419, 5701, 5987, 6079, 6529, 7127, 7639, 7753, 7853, 9343, 9433, 10499, 10781, 10831, 11131, 11489, 12619, 13523, 14083, 15227, 15937, 19501, 22247, 22511

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 13 is a term because 13, 17, 19, 23 are consecutive primes and A001414(19+23) = A001414(2*3*7) = 12 divides 13+17+19+23 = 72.

Maple

q:= 2: r:= 3: s:= 5:
R:= NULL: count:= 0:
while count < 50 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  a:= add(t[1]*t[2], t = ifactors(r+s)[2]);
  if (p+q+r+s) mod a = 0 then count:= count+1; R:= R, p fi
od:
R;

Mathematica

Select[Partition[Prime[Range[2600]], 4, 1], Divisible[Total[#], Total[Times@@@FactorInteger[ Total[ Take[#, -2]]]]]&][[;; , 1]] (* Harvey P. Dale, Feb 11 2024 *)

Crossrefs

Cf. A001414, A352459, A352480.

Sequence in context: A032481 A365502 A348313 * A236411 A073615 A346147

Adjacent sequences: A352531 A352532 A352533 * A352535 A352536 A352537

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 20 2022

Status

approved