A341271 a(n) is the least k such that there are distinct primes p,q,r,s such that k-p, k-q, k-r, k-s are primes and (p+q)/(r+s) = n.

16, 18, 16, 36, 34, 34, 48, 46, 46, 66, 64, 76, 108, 64, 64, 108, 104, 76, 144, 106, 110, 144, 106, 106, 156, 112, 112, 186, 142, 142, 198, 154, 154, 234, 154, 154, 276, 184, 184, 246, 196, 230, 318, 184, 184, 288, 202, 196, 318, 232, 232, 318, 244, 244, 354, 274, 232, 354, 244, 244, 426, 274

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..249

Example

a(4) = 36 because 4 = (17+31)/(5+7) where 17,31,5,7 are primes and 36-17 = 19, 36-31 = 5, 36-5 = 31 and 36-7 = 29 are primes, and 36 is the least number k for which such primes exist.

Maple

f:= proc(n) local P, i, c1, c2;
  P:= select(t -> isprime(t) and isprime(n-t), {seq(i, i=3..n, 2)});
  select(type, {seq(seq(convert(c1, `+`)/convert(c2, `+`), c1 = combinat:-choose(P minus c2, 2)), c2 = combinat:-choose(P, 2))}, integer)
end proc:
N:= 70: # for a(1)..a(N)
V:= Vector(N): count:= 0:
for n from 2 by 2 while count < N do
  for v in f(n) do
    if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi
od od:
convert(V, list);

Crossrefs

Sequence in context: A030046 A002925 A070540 * A358677 A085096 A043675

Adjacent sequences: A341268 A341269 A341270 * A341272 A341273 A341274

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 07 2021

Status

approved