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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 Table of n, a(n) for n=1..6. 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 Cf. A001358, A092192, A370162, A370685. Sequence in context: A198156 A347818 A273517 * A003086 A102958 A321795 Adjacent sequences: A370684 A370685 A370686 * A370688 A370689 A370690 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.)