A067381 -id:A067381 - cp's OEIS frontend

A067375 Integers expressible as the sum of (at least two) consecutive primes in at least 5 ways.

16277, 20272, 25416, 28500, 34421, 41074, 45101, 46660, 50560, 53424, 59068, 68787, 70104, 70692, 71548, 78756, 85433, 85481, 88453, 94350, 98881, 105827, 117907, 120151, 121847, 125952, 130638, 130789, 131420, 132539, 133367, 134376, 135918, 139853, 158810

Offset: 1

Patrick De Geest, Feb 04 2002

nonn

			E.g. 16277 = (#7,2297) (#11,1451) (#13,1213) (#35,359) (#37,331).

Donovan Johnson, Table of n, a(n) for n = 1..1000
P. De Geest, WONplate 122
C. Rivera, Puzzle 46

Cf. A050936, A067372-A067381, A055000.

t={};Do[p=Prime[m];Do[p=p+Prime[n];If[p<200000,AppendTo[t,p]],{n,m+1,7001}],{m,1,7000}];t=Sort@t;f5[l_]:=Module[{t={}},Do[If[l[[n]]==l[[n+4]],AppendTo[t,l[[n]]]],{n,Length[l]-4}];t];Union@f5[t] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

A084143(a(n)) > 4. - Ray Chandler, Sep 20 2023

Offset and a(35) corrected by Donovan Johnson, Nov 14 2013

A067376 Smallest integer expressible as the sum of (at least two) consecutive primes in n ways.

Original entry on oeis.org

5, 36, 240, 311, 16277, 130638, 218918, 9186778, 274452156, 4611108324, 12941709050

Offset: 1

Patrick De Geest, Feb 04 2002

a(10)-a(11) found by Wilfred Whiteside in 2007 (see Rivera link). - Michael S. Branicky, Jul 27 2022

			In n=7 ways: 218918 = (#12,18199) (#16,13619) (#22,9851) (#28,7691) (#38,5623) (#46,4561) (#62,3301).

Patrick De Geest, WONplate 122
Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.

Cf. A050936, A067372-A067381, A054859.

Offset corrected and a(8)-a(9) from Donovan Johnson, Mar 14 2010

a(10) confirmed and a(10)-a(11) entered by Michael S. Branicky, Jul 27 2022

A350334 Primes expressible as the sum of (at least two) consecutive primes in at least 6 ways.

Original entry on oeis.org

442019, 1866373, 3051161, 3634531, 3704819, 3839677, 3890609, 4539331, 4711937, 5011213, 5069023, 5369743, 5384221, 6137587, 6783263, 6893273, 9213073, 10354177, 10602763, 11394193, 11849339, 12012257, 13126801, 13322887, 14385781, 15077143, 17225003, 19301221

Offset: 1

Jon E. Schoenfield, Dec 25 2021

nonn

Subsequence of A164556.

			442019 is a term because it is a prime and
   442019 = Sum_{j=13620..13622} prime(j)
          = Sum_{j=5044..5052} prime(j)
          = Sum_{j=2019..2043} prime(j)
          = Sum_{j=1573..1605} prime(j)
          = Sum_{j=954..1010} prime(j)
          = Sum_{j=81..381} prime(j).

Cf. A067377, A067378, A067379, A067380, A067381, A164556.

A350335 Primes expressible as the sum of (at least two) consecutive primes in at least 7 ways.

Original entry on oeis.org

3634531, 27411611, 28127521, 28445689, 48205429, 54604973, 56857523, 63461429, 70734089, 72087167, 75489781, 82183951, 83020733, 89752433, 92712023, 94026311, 100925263, 111282419, 137392361, 163506407, 164711999, 194039771, 195327179, 196364899, 196876789

Offset: 1

Jon E. Schoenfield, Dec 25 2021

nonn

Subsequence of A350334.

			3634531 is a term because it is a prime and
   3634531 = Sum_{j=42997..43003} prime(j)
           = Sum_{j=15749..15769} prime(j)
           = Sum_{j=7294..7342} prime(j)
           = Sum_{j=7032..7082} prime(j)
           = Sum_{j=3397..3509} prime(j)
           = Sum_{j=165..1003} prime(j)
           = Sum_{j=65..995} prime(j).

Cf. A067377, A067378, A067379, A067380, A067381, A164556, A350334.

A372507 a(n) is the smallest number k such that prime(k) is expressible as the sum of (at least two) consecutive primes in n ways.

Original entry on oeis.org

3, 13, 64, 64, 3677, 37096, 259073, 2899722, 88790445, 1554106234, 6711446232, 215580239668

Offset: 1

Ilya Gutkovskiy, May 04 2024

Cf. A000040, A000720, A054859, A067376, A067381, A348791.

a(n) = A000720(A067381(n)).

cp's OEIS Frontend

A067375 Integers expressible as the sum of (at least two) consecutive primes in at least 5 ways.

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A067376 Smallest integer expressible as the sum of (at least two) consecutive primes in n ways.

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A350334 Primes expressible as the sum of (at least two) consecutive primes in at least 6 ways.

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A350335 Primes expressible as the sum of (at least two) consecutive primes in at least 7 ways.

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A372507 a(n) is the smallest number k such that prime(k) is expressible as the sum of (at least two) consecutive primes in n ways.

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