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

24, 749, 48, 311, 690, 251, 2706, 2773, 6504, 1081, 2162, 1753, 11356, 6223, 1392, 2303, 9838, 637, 14510, 1995, 3154, 21459, 72960, 5691, 8140, 1475, 2350, 3647, 1593, 7607, 55074, 2719, 9852, 12143, 106562, 12615, 9036, 19883, 15438, 28369, 8560, 8415, 3831

Offset

2,1

Comments

The sequence is non-monotone.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Example

a(2) = 24 = A000040(5) + A000040(6) = 11 + 13 = A001358(4) + A001358(5) = 10 + 14,
a(3) = 749 = A000040(53) + A000040(54) + A000040(55) = 241 + 251 + 257 = A001358(79) + A001358(80) + A001358(81) = 247 + 249 + 253.

Maple

issp:= n-> is(not isprime(n) and numtheory[bigomega](n)=2):
ithsp:= proc(n) option remember; local k; for k from 1+
        `if`(n=1, 1, ithsp(n-1)) while not issp(k) do od; k
        end:
ps:= proc(i, j) option remember;
       ithprime(j)+`if`(i=j, 0, ps(i, j-1))
     end:
ss:= proc(i, j) option remember;
       ithsp(j)+`if`(i=j, 0, ss(i, j-1))
     end:
a:= proc(n) option remember; local i, j, k, l, p, s;
      i, j, k, l, p, s:= 1, n, 1, n, ps(1, n), ss(1, n);
      do if p=s then return p
       elif p<s then i:=i+1; j:=j+1; p:= ps(i, j)
       else          k:=k+1; l:=l+1; s:= ss(k, l)
      fi od
    end:
seq(a(n), n=2..50);  # Alois P. Heinz, Mar 24 2017

Mathematica

sp=Select[Range[4, 100000], 2==PrimeOmega[#]&]; pr=Prime[Range[PrimePi[Max[sp]]]];
Table[Intersection[(Total/@Partition[pr, k, 1]), Total/@Partition[sp, k, 1]][[1]], {k, 2, 100}}

Crossrefs

Cf. A000040 Primes, A001358 Semiprimes, A118717 Sum of two consecutive semiprimes.

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.

Sequence in context: A279659 A062528 A175604 * A359480 A361661 A269147

Adjacent sequences: A283870 A283871 A283872 * A283874 A283875 A283876

Keyword

nonn

Author

Zak Seidov, Mar 17 2017

Extensions

More terms from Alois P. Heinz, Mar 24 2017

Status

approved