cp's OEIS Frontend

A283873 Smallest number that is the sum of n successive primes and also the sum of n successive semiprimes, n > 1.

%I A283873 #20 Jun 16 2025 08:49:09
%S A283873 24,749,48,311,690,251,2706,2773,6504,1081,2162,1753,11356,6223,1392,
%T A283873 2303,9838,637,14510,1995,3154,21459,72960,5691,8140,1475,2350,3647,
%U A283873 1593,7607,55074,2719,9852,12143,106562,12615,9036,19883,15438,28369,8560,8415,3831
%N A283873 Smallest number that is the sum of n successive primes and also the sum of n successive semiprimes, n > 1.
%C A283873 The sequence is non-monotone.
%H A283873 Alois P. Heinz, <a href="/A283873/b283873.txt">Table of n, a(n) for n = 2..1000</a>
%e A283873 a(2) = 24 = A000040(5) + A000040(6) = 11 + 13 = A001358(4) + A001358(5) = 10 + 14,
%e A283873 a(3) = 749 = A000040(53) + A000040(54) + A000040(55) = 241 + 251 + 257 = A001358(79) + A001358(80) + A001358(81) = 247 + 249 + 253.
%p A283873 issp:= n-> is(not isprime(n) and numtheory[bigomega](n)=2):
%p A283873 ithsp:= proc(n) option remember; local k; for k from 1+
%p A283873         `if`(n=1, 1, ithsp(n-1)) while not issp(k) do od; k
%p A283873         end:
%p A283873 ps:= proc(i, j) option remember;
%p A283873        ithprime(j)+`if`(i=j, 0, ps(i, j-1))
%p A283873      end:
%p A283873 ss:= proc(i, j) option remember;
%p A283873        ithsp(j)+`if`(i=j, 0, ss(i, j-1))
%p A283873      end:
%p A283873 a:= proc(n) option remember; local i, j, k, l, p, s;
%p A283873       i, j, k, l, p, s:= 1, n, 1, n, ps(1, n), ss(1, n);
%p A283873       do if p=s then return p
%p A283873        elif p<s then i:=i+1; j:=j+1; p:= ps(i, j)
%p A283873        else          k:=k+1; l:=l+1; s:= ss(k, l)
%p A283873       fi od
%p A283873     end:
%p A283873 seq(a(n), n=2..50);  # _Alois P. Heinz_, Mar 24 2017
%t A283873 sp=Select[Range[4,100000],2==PrimeOmega[#]&];pr=Prime[Range[PrimePi[Max[sp]]]];
%t A283873 Table[Intersection[(Total/@Partition[pr,k,1]),Total/@Partition[sp,k,1]][[1]],{k,2,100}]
%Y A283873 Cf. A000040 Primes, A001358 Semiprimes, A118717 Sum of two consecutive semiprimes.
%Y A283873 Sum of k consecutive primes: A001043 k=2, A034961 k=3, A034963 k=4, A034964 k=5, A127333 k=6, A127334 k=7, A127335 k=8, A127336 k=9, A127337 k=10, A127338 k=11, A127339 k=12.
%K A283873 nonn
%O A283873 2,1
%A A283873 _Zak Seidov_, Mar 17 2017
%E A283873 More terms from _Alois P. Heinz_, Mar 24 2017