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A206854 Smallest integer m such that m is a product of 2n-1 consecutive primes and a sum of 2n-1 consecutive primes. 0
2, 33263, 2775683761181, 52139749485151463, 31359251876786281892441299570699, 2385018819218440287149, 23509572623777698757692123744388316389653416929069870587, 436178570920976645136650311902311012102337977560516289614008518576769313, 166345108784858794943225366868487068031523855419640057875257310044811 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
n=1: m = 2 (trivial case: product and sum of single prime, 2);
n=2: m = 33263 = product{29, 31, 37} = sum{11083, 11087, 11093};
n=3: m = 2775683761181 = product({293, 307, 311, 313, 317}) = sum({555136752211, 555136752221, 555136752227, 555136752251, 555136752271});
n=4: m = 52139749485151463=product({229, 233, 239, 241, 251, 257, 263})= sum({7448535640735789, 7448535640735843, 7448535640735867, 7448535640735877, 7448535640735991, 7448535640736009, 7448535640736087});
n=5: m = 31359251876786281892441299570699 = product({3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191}) = sum({3484361319642920210271255507593, 3484361319642920210271255507619, 3484361319642920210271255507719, 3484361319642920210271255507767, 3484361319642920210271255507923, 3484361319642920210271255507937, 3484361319642920210271255507941, 3484361319642920210271255508067, 3484361319642920210271255508133});
n=6: m = 2385018819218440287149 = product({67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109}) = sum({216819892656221844131, 216819892656221844133, 216819892656221844139, 216819892656221844169, 216819892656221844307, 216819892656221844331, 216819892656221844347, 216819892656221844373, 216819892656221844397, 216819892656221844401, 216819892656221844421}).
LINKS
MAPLE
scp:= proc(x, n) local P, i, s;
P:= Vector(n);
P[1]:= nextprime(ceil(x/n));
for i from 2 to n do P[i]:= nextprime(P[i-1]) od;
s:= convert(P, `+`);
while s > x do
s:= s - P[n];
P[2..n]:= P[1..n-1];
if P[2] = 2 then return false fi;
P[1]:= prevprime(P[2]);
s:= s + P[1];
od;
evalb(s=x)
end proc:
f:= proc(n) local i, P, r;
P:= <seq(ithprime(i), i=1..2*n-1)>;
r:= convert(P, `*`);
while not scp(r, 2*n-1) do
r:= r/P[1];
P[1..2*n-2]:= P[2..2*n-1];
P[2*n-1]:= nextprime(P[2*n-2]);
r:= r*P[2*n-1];
od;
end proc:
f(1):= 2:
map(f, [$1..8]); # Robert Israel, Mar 13 2023
CROSSREFS
Cf. A203619.
Sequence in context: A030462 A228556 A001377 * A330304 A272166 A291881
KEYWORD
nonn
AUTHOR
Zak Seidov, Feb 13 2012
EXTENSIONS
a(7)-a(9) from Robert Israel, Mar 13 2023
STATUS
approved

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Last modified May 30 03:30 EDT 2024. Contains 372957 sequences. (Running on oeis4.)