A215991 -id:A215991 - cp's OEIS frontend

A070934 Smallest prime equal to the sum of 2n+1 consecutive primes.

2, 23, 53, 197, 127, 233, 691, 379, 499, 857, 953, 1151, 1259, 1583, 2099, 2399, 2417, 2579, 2909, 3803, 3821, 4217, 4651, 5107, 5813, 6829, 6079, 6599, 14153, 10091, 8273, 10163, 9521, 12281, 13043, 11597, 12713, 13099, 16763, 15527, 16823, 22741

Offset: 0

Lekraj Beedassy, May 21 2002

nonn

			Every term of the increasing sequence of primes 127, 401, 439, 479, 593,... is splittable into a sum of 9 consecutive odd primes and 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 is the least one corresponding to n = 4.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. Bisection of A070281.
See A082244 for another version.
Cf. A089793, A215235.
Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.

f[n_] := Block[{k = 1, s},While[s = Sum[Prime[i], {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[f[n], {n, 0, 41}] (* Ray Chandler, Sep 27 2006 *)

Corrected and extended by Ray G. Opao, Aug 26 2004

Entry revised by Ray Chandler, Sep 27 2006

A082244 Smallest odd prime that is the sum of 2n+1 consecutive primes.

Original entry on oeis.org

3, 23, 53, 197, 127, 233, 691, 379, 499, 857, 953, 1151, 1259, 1583, 2099, 2399, 2417, 2579, 2909, 3803, 3821, 4217, 4651, 5107, 5813, 6829, 6079, 6599, 14153, 10091, 8273, 10163, 9521, 12281, 13043, 11597, 12713, 13099, 16763, 15527, 16823, 22741

Offset: 0

Cino Hilliard, May 09 2003

			For n = 2,
2+3+5+7+11=28
3+5+7+11+13=39
5+7+11+13+17=53
so 53 is the first prime that is the sum of 5 consecutive primes

Robert Israel, Table of n, a(n) for n = 0..10000

See A070934 for another version.

Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.

P:= select(isprime, [seq(i,i=3..3000,2)]):
S:= [0,op(ListTools:-PartialSums(P))]: nS:= nops(S):
R:= NULL:
for n from 1 do
  found:= false;
  for j from 1 to nS - 2*n + 1 while not found do
    v:= S[j+2*n-1]-S[j];
    if isprime(v) then R:= R,v; found:= true fi
  od;
  if not found then break fi;
od:
R; # Robert Israel, Jan 09 2025

Join[{3},Table[SelectFirst[Total/@Partition[Prime[Range[1000]],2n+1,1],PrimeQ],{n,50}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 15 2016 *)

\\ First prime that the sum of an odd number of consecutive primes
psumprm(n) = { sr=0; forstep(i=1,n,2, s=0; for(j=1,i, s+=prime(j); ); for(x=1,n, s = s - prime(x)+ prime(x+i); if(isprime(s),sr+=1.0/s; print1(s" "); break); ); ); print(); print(sr) }

The sum of the reciprocals = 0.4304...

A342439 Let S(n,k) denote the set of primes < 10^n which are the sum of k consecutive primes, and let K = maximum k >= 2 such that S(n,k) is nonempty; then a(n) = max S(n,K).

Original entry on oeis.org

5, 41, 953, 9521, 92951, 997651, 9964597, 99819619, 999715711, 9999419621, 99987684473, 999973156643, 9999946325147, 99999863884699, 999999149973119, 9999994503821977, 99999999469565483, 999999988375776737, 9999999776402081701

Offset: 1

Bernard Schott, Mar 12 2021

Inspired by the 50th problem of Project Euler (see link).
There must be at least two consecutive primes in the sum.
The corresponding number K of consecutive primes to get this largest prime is A342440(n) and the first prime of these A342440(n) consecutive primes is A342453(n).
It can happen that the sums of K = A342440(n) consecutive primes give two (or more) distinct n-digit primes. In that case, a(n) is the greatest of these primes. Martin Ehrenstein proved that there are only two such cases when 1 <= n <= 19, for n = 7 and n = 15 (see corresponding examples).
Solutions and Python program are proposed in Dreamshire and Archive.today links. - Daniel Suteu, Mar 12 2021

			a(1) = 5 = 2+3.
a(2) = 41 = 2 + 3 + 5 + 7 + 11 + 13; note that 97 = 29 + 31 + 37 is prime, sum of 3 consecutive primes, but 41 is obtained by adding 6 consecutive primes, so, 97 is not a term.
A342440(7) = 1587, and there exist two 7-digit primes that are sum of 1587 consecutive primes; as 9951191 = 5+...+13399 < 9964597 = 7+...+13411 hence a(7) = 9964597.
A342440(15) = 10695879 , and there exist two 15-digit primes that are sum of 10695879 consecutive primes; as 999998764608469 = 7+...+192682309 < 999999149973119 = 13+...+192682337, hence a(15) = 999999149973119.

Dreamshire, Project Euler 50 Solution.
Archive.today, trizen / experimental-projects.
Project Euler, Problem 50: Consecutive prime sum.

Cf. A034962, A034965, A082246, A082251, A127340, A127341, A215991, A067377.

Cf. A342440, A342443, A342444, A342453, A342454.

Name improved by N. J. A. Sloane, Mar 12 2021
a(4)-a(17) from Daniel Suteu, Mar 12 2021
a(18)-a(19) from Martin Ehrenstein, Mar 13 2021
a(7) and a(15) corrected by Martin Ehrenstein, Mar 15 2021

A216020 Primes that are the sum of 100001 consecutive primes.

Original entry on oeis.org

62308795099, 62312695301, 62332197553, 62349100789, 62356902719, 62371207153, 62423231159, 62425832657, 62457052223, 62458353173, 62459654141, 62464858003, 62479168853, 62483071967, 62499986407, 62502588679, 62507793281, 62510395583, 62512997927, 62526009929

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

Select[Total/@Partition[Prime[Range[120000]],100001,1],PrimeQ] (* Harvey P. Dale, Jun 06 2018 *)

More terms added from b-file by Andrew Howroyd, Feb 19 2018

A215992 Primes that are the sum of 51 consecutive primes.

Original entry on oeis.org

6829, 7853, 9473, 10037, 10601, 12041, 12329, 12917, 13217, 13523, 14713, 16493, 17099, 21179, 21503, 23459, 24091, 24419, 26321, 29243, 29567, 30223, 30881, 32237, 32939, 33623, 33961, 34301, 34651, 35677, 36013, 36997, 42221, 44371, 44729

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

A215993 Primes that are the sum of 101 consecutive primes.

Original entry on oeis.org

37447, 38047, 44203, 48611, 49253, 60259, 60923, 68281, 74297, 82421, 84503, 86599, 91423, 92831, 99761, 108533, 120811, 125887, 126613, 128761, 129469, 133781, 134507, 138863, 139591, 150827, 159161, 160697, 163003, 164531, 170633, 173741, 175277, 176797

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

Select[Total/@Partition[Prime[Range[1000]],101,1],PrimeQ] (* Harvey P. Dale, Sep 06 2012 *)

More terms from Harvey P. Dale, Sep 06 2012

A215994 Primes that are the sum of 151 consecutive primes.

Original entry on oeis.org

71011, 71941, 80429, 88079, 106699, 107699, 114761, 117809, 123863, 126949, 134287, 137437, 143719, 148961, 157457, 160627, 170063, 181871, 189467, 200467, 216023, 219377, 221603, 222713, 223829, 224951, 229433, 231661, 238373, 241727, 244009, 254383, 264731

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

Select[Total/@Partition[Prime[Range[500]],151,1],PrimeQ] (* Harvey P. Dale, May 14 2017 *)

More terms from Harvey P. Dale, May 14 2017

A215995 Primes that are the sum of 201 consecutive primes.

Original entry on oeis.org

115279, 130457, 131731, 135613, 162293, 163637, 164987, 173149, 179957, 201961, 204733, 214517, 230137, 231559, 232987, 244547, 257591, 259033, 267791, 273643, 283937, 292841, 313763, 319763, 322769, 325769, 336211, 342187, 349709, 352757, 371233, 372797

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

Select[Total/@Partition[Prime[Range[2000]],201,1],PrimeQ] (* Harvey P. Dale, Nov 23 2016 *)

More terms from Harvey P. Dale, Nov 23 2016

A215996 Primes that are the sum of 251 consecutive primes.

Original entry on oeis.org

198197, 199831, 204751, 208057, 216373, 218047, 219721, 224771, 229837, 247001, 248723, 250451, 262657, 269701, 330439, 352411, 363379, 367021, 385351, 387187, 389047, 415409, 421121, 434377, 440023, 441907, 449419, 453181, 458863, 468271, 483389, 487183

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

Select[Total/@Partition[Prime[Range[600]],251,1],PrimeQ] (* Harvey P. Dale, Oct 18 2013 *)

More terms from Harvey P. Dale, Oct 18 2013

A215997 Primes that are the sum of 301 consecutive primes.

Original entry on oeis.org

289099, 295201, 299287, 301331, 305419, 307471, 309523, 317771, 319831, 361961, 376921, 387623, 406969, 413461, 422209, 426583, 442019, 459817, 475369, 513067, 519769, 526501, 533257, 535511, 537773, 594821, 608759, 629689, 636697, 646013, 648341, 678883

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A215991.

More terms added from b-file by Andrew Howroyd, Feb 11 2018

cp's OEIS Frontend

A070934 Smallest prime equal to the sum of 2n+1 consecutive primes.

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A082244 Smallest odd prime that is the sum of 2n+1 consecutive primes.

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A342439 Let S(n,k) denote the set of primes < 10^n which are the sum of k consecutive primes, and let K = maximum k >= 2 such that S(n,k) is nonempty; then a(n) = max S(n,K).

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A216020 Primes that are the sum of 100001 consecutive primes.

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A215992 Primes that are the sum of 51 consecutive primes.

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A215993 Primes that are the sum of 101 consecutive primes.

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A215994 Primes that are the sum of 151 consecutive primes.

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Mathematica

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A215995 Primes that are the sum of 201 consecutive primes.

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Programs

Mathematica

Extensions

A215996 Primes that are the sum of 251 consecutive primes.

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