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A331586 Even numbers n such that A048633(n+1) = A048633(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A168349 A179136 A249432 * A077395 A185534 A185526
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 21 2020
STATUS
approved

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Last modified April 21 07:35 EDT 2024. Contains 371850 sequences. (Running on oeis4.)