A092189 -id:A092189 - cp's OEIS frontend

A062198 Sum of first n semiprimes.

4, 10, 19, 29, 43, 58, 79, 101, 126, 152, 185, 219, 254, 292, 331, 377, 426, 477, 532, 589, 647, 709, 774, 843, 917, 994, 1076, 1161, 1247, 1334, 1425, 1518, 1612, 1707, 1813, 1924, 2039, 2157, 2276, 2397, 2519, 2642, 2771, 2904, 3038, 3179, 3321, 3464

Offset: 1

Shyam Sunder Gupta, Aug 24 2003

Elements in this sequence can themselves be semiprimes. a(1) = 4 = 2^2. a(2) = 10 = 2 * 5. a(6) = 58 = 2 * 29. a(11) = 185 = 5 * 37. a(12) = 219 = 3 * 73. a(13) = 254 = 2 * 127. a(16) = 377 = 13 * 29. a(20) = 589 = 19 * 31. Etc. Does this happen infinitely often? - Jonathan Vos Post, Dec 11 2004

			a(4) = 29 because the sum of the first 4 semiprimes 4+6+9+10 is 29.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A092189, A092190.

Accumulate[Select[Range[200],PrimeOmega[#]==2&]] (* Harvey P. Dale, Jul 23 2014 *)

is_A062198(N)={ my(n=0); while(N>0, while(bigomega(n++)!=2, ); N-=n); !N}  \\ - M. F. Hasler, Sep 23 2012

A062198(n, list)={my(s=0, N=0); until(!n--, until(bigomega(N++)==2, ); s+=N; list & print1(s", ")); s}  \\ - M. F. Hasler, Sep 23 2012

a(n) = Sum_{i=1..n} A001358(i). - R. J. Mathar, Sep 14 2012

A092190 Semiprimes that are the sum of the first n semiprimes for some n.

Original entry on oeis.org

4, 10, 58, 185, 219, 254, 377, 589, 843, 917, 1247, 1707, 2157, 2519, 2642, 2771, 3755, 4227, 5078, 5633, 6433, 6638, 7053, 9031, 15469, 16109, 17414, 18763, 19109, 21281, 22421, 23591, 26827, 28093, 35489, 35978, 36471, 37469, 38987, 41578, 42634

Offset: 1

Zak Seidov, Feb 23 2004

			10 is a term because the sum of the first two semiprimes 4 and 6 is 10.

Zak Seidov, Table of n, a(n) for n = 1..5000

Corresponding values of n: A092189.

s = Select[Range@ 40882, PrimeOmega@ # == 2 &]; Select[Accumulate[s[[1 ;; 164]]], PrimeOmega@ # == 2 &] (* Michael De Vlieger, Sep 21 2015 *)

is_A092190(N)={bigomega(N)==2 & is_A062198(N)}  \\ M. F. Hasler, Sep 23 2012

A092190(n,list=0,b=2)={my(s=0,N=0); while(n, until(bigomega(N++)==b,); bigomega(s+=N)==b & n-- & list & print1(s",")); s}  \\ M. F. Hasler, Sep 23 2012

Equals A062198 intersect A001358. - M. F. Hasler, Sep 23 2012

A213650 Numbers k such that the sum of the first k primes is semiprime.

Original entry on oeis.org

3, 7, 8, 10, 16, 18, 22, 28, 32, 34, 36, 38, 44, 46, 48, 54, 55, 58, 59, 65, 66, 72, 75, 82, 92, 93, 94, 104, 106, 110, 118, 120, 133, 136, 137, 138, 140, 141, 142, 144, 148, 150, 154, 156, 164, 168, 170, 174, 190, 194, 202, 210, 212, 218, 224, 226, 232, 234

Offset: 1

Michel Lagneau, Jun 17 2012

nonn

Numbers k such that A007504(k) is included in A001358.

			8 is in the sequence because the sum of the first 8 primes is  2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 = 7*11, which is semiprime.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001358, A007504, A013916, A092189 (numbers n such that sum of first n semiprimes is a semiprime), A092190 (semiprimes that are the sum of first n semiprimes for some n), A180152 (numbers n such that the sum of the first n semiprimes is a prime).

with(numtheory): for n from 1 to 500 do:s:=sum(‘ithprime(k)’, ’k’=1..n):if bigomega(s)=2 then printf(`%d, `, n):else fi:od:

Flatten[Position[Accumulate[Prime[Range[300]]],_?(PrimeOmega[#]==2&)]]

isok(n) = bigomega(vecsum(primes(n))) == 2; \\ Michel Marcus, Sep 18 2017

A265438 Smallest semiprime that is the sum of n consecutive semiprimes.

Original entry on oeis.org

4, 10, 25, 39, 69, 58, 133, 122, 249, 209, 185, 219, 254, 327, 458, 377, 473, 579, 745, 589, 951, 898, 1047, 843, 917, 1382, 1157, 1243, 1247, 1678, 1514, 1895, 1703, 1707, 2138, 2147, 2599, 2157, 2509, 2515, 2519, 2642, 2771, 3566, 4126, 3317, 3599, 3891, 4198, 3755, 4369, 4223, 4227

Offset: 1

Zak Seidov, Dec 09 2015

nonn

The sequence is non-monotonic. But are all the terms distinct?

A092190 is a subsequence. More precisely, a(A092189(k)) = A092190(k). - Altug Alkan, Dec 13 2015

			a(1) = 4 = A001358(1),
a(2) = 10 = A001358(3) = A092192(1) = A001358(1)+A001358(2) = 4+6,
a(3) = 25 = A001358(9) = A131610(1),
a(4) = 39 = A001358(15) = A158339(1),
a(5) = 69 = A001358(24) = A254712(1),
a(6) = 58 = A001358(21) = A266451(1).

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A001358, A092190, A092192, A131610, A158339, A254712.

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A062198 Sum of first n semiprimes.

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A092190 Semiprimes that are the sum of the first n semiprimes for some n.

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A213650 Numbers k such that the sum of the first k primes is semiprime.

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A265438 Smallest semiprime that is the sum of n consecutive semiprimes.

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