A331586 Even numbers n such that A048633(n+1) = A048633(n).

174, 398, 474, 934, 1214, 1934, 2254, 2638, 2966, 3806, 3886, 4024, 4574, 4696, 4718, 4928, 4958, 4990, 5014, 5246, 5290, 5438, 6698, 6934, 7028, 7136, 7258, 7266, 7424, 7694, 7838, 8176, 8448, 8574, 8720, 8958, 9854, 9974, 10174, 10334, 10448, 11338, 11374, 12094, 12102, 12220, 12462, 12626

Offset

1,1

Comments

binomial(2k+1,k)/binomial(2k,k) = (2k+1)/(k+1), so 2k is a member if and only if every prime dividing 2k+1 divides binomial(2k,k) and every prime dividing k+1 divides binomial(2k+1,k).

A048633(n+1)=A048633(n) for all odd numbers n except the Mersenne numbers (A000225).

Links

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

Example

a(1)=174 is a member because 174 is even and A048633(174)=A048633(175)=632127493640977953733428652337034082437215015190.

Maple

g:= proc(m, n, p)
  local Lm, Ln;
   Lm:= convert(m, base, p);
   Ln:= convert(n, base, p);
   min(Lm[1..nops(Ln)]-Ln) < 0
end proc:
filter:= proc(n) local p;
  for p in numtheory:-factorset(n+1) do
     if not g(n, n/2, p) then return false fi;
  od;
  for p in numtheory:-factorset(n/2+1) do
     if not g(n+1, n/2, p) then return false fi
  od;
  true
end proc:
select(filter, [seq(i, i=2..15000, 2)]);

Crossrefs

Cf. A000225, A048633.

Sequence in context: A168349 A179136 A249432 * A077395 A185534 A185526

Adjacent sequences: A331583 A331584 A331585 * A331587 A331588 A331589

Keyword

nonn

Author

Robert Israel, Jan 21 2020

Status

approved