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A370687 a(n) is the first number that is the sum of k successive semiprimes for 1 <= k <= n. 0
4, 10, 134, 2045, 2705, 16626281 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(7) > 5 * 10^8 if it exists.
LINKS
EXAMPLE
a(3) = 134 because 134 = 2 * 67 is a semiprime, the sum of two successive semiprimes 65 = 5 * 13 and 69 = 3 * 23, and the sum of three successive semiprimes 39 = 3 * 13, 46 = 2 * 23, 49 = 7 * 7, and is the least such number.
MAPLE
N:= 2*10^7: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N/2, 2)]):
nP:= nops(P):
SP:= 0:
for i from 1 while P[i]^2 <= N do
m:= ListTools:-BinaryPlace(P, N/P[i]);
SP:= SP, op(P[i]*P[i..m]);
od:
SP:= sort([SP]):
SS:= ListTools:-PartialSums(SP):
V:= Vector(6):
SI:= Vector(6):
II:= Vector(6, 1):
for i from 1 to 6 do SI[i]:= SS[i+1]-SS[1] od:
count:= 1: V[1]:= 4: m:= 4: im:= {1}:
while count < 6 do
for j in im do
II[j]:= II[j]+1;
SI[j]:= SS[II[j]+j] - SS[II[j]];
od;
m:= min(SI);
im:= select(j -> SI[j] = m, {$1..20});
for k from 1 to 20 while {$1..k} subset im do
if V[k] = 0 then V[k]:= m; count:= count+1 fi
od;
od:
convert(V, list);
CROSSREFS
Sequence in context: A198156 A347818 A273517 * A003086 A102958 A321795
KEYWORD
nonn,more
AUTHOR
Robert Israel, Feb 27 2024
STATUS
approved

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Last modified June 22 05:36 EDT 2024. Contains 373565 sequences. (Running on oeis4.)