A082251 -id:A082251 - cp's OEIS frontend

A215991 Primes that are the sum of 25 consecutive primes.

1259, 1361, 2027, 2267, 2633, 3137, 3389, 4057, 5153, 6257, 6553, 7013, 7451, 7901, 9907, 10499, 10799, 10949, 11579, 12401, 14369, 15013, 15329, 17377, 17903, 18251, 18427, 19309, 22441, 24023, 25057, 25229, 26041, 26699, 28111, 29017, 29207, 30707, 32939, 35051, 36583

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

Such sequences already existed for all odd numbers <= 15. I chose the particular points (in A215991-A216020) so that by referring to a particular n-th term of one of these sequences, the expected range of the n-th term of an x-prime sum can be calculated for any odd x<100000.

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

Cf. A034962, A034965, A082246, A082251, A127340, A127341, A161612, A215992, A215993, A215994, A215995, A215996, A215997, A215998, A215999, A216000, A216001, A216002, A216003, A216004, A216005, A216006, A216007, A216008, A216009, A216010, A216011, A216012, A216013, A216014, A216015, A216016, A216017, A216018, A216019, A216020.

P:=Filtered([1..10^4],IsPrime);;
Filtered(List([0..250],k->Sum([1..25],i->P[i+k])),IsPrime); # Muniru A Asiru, Feb 11 2018

select(isprime, [seq(add(ithprime(i+k), i=1..25), k=0..250)]); # Muniru A Asiru, Feb 11 2018

Select[ListConvolve[Table[1, 25], Prime[Range[500]]], PrimeQ] (* Jean-François Alcover, Jul 01 2018, after Harvey P. Dale *)
Select[Total/@Partition[Prime[Range[300]],25,1],PrimeQ] (* Harvey P. Dale, Mar 04 2023 *)

psumprm(m, n)={my(list=List(), s=sum(j=1,m,prime(j)), i=1); while(#listAndrew Howroyd, Feb 11 2018

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

Original entry on oeis.org

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

A127336 Numbers that are the sum of 9 consecutive primes.

Original entry on oeis.org

100, 127, 155, 187, 221, 253, 287, 323, 363, 401, 439, 479, 515, 553, 593, 635, 679, 721, 763, 803, 841, 881, 929, 977, 1025, 1067, 1115, 1163, 1213, 1267, 1321, 1367, 1415, 1459, 1511, 1555, 1601, 1643, 1691, 1747, 1801, 1851, 1903, 1951, 1999, 2053

Offset: 1

Artur Jasinski, Jan 11 2007

a(n) = absolute value of coefficient of x^8 of the polynomial Product_{j=0..8}(x - prime(n+j)) of degree 9; the roots of this polynomial are prime(n), ..., prime(n+8).

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127337, A127338, A127339, A082251, A228200.

[&+[ NthPrime(n+k): k in [0..8] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011

A127336 = {}; Do[AppendTo[A127336, Sum[Prime[x + n], {n, 0, 8}]], {x, 1, 50}]; A127336 (* Artur Jasinski, Jan 11 2007 *)
Table[Plus@@Prime[Range[n, n + 8]], {n, 50}] (* Alonso del Arte, Aug 27 2013 *)
Total/@Partition[Prime[Range[60]],9,1] (* Harvey P. Dale, Nov 18 2020 *)

{m=46;k=9;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007
{m=46;k=9;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 13 2007

from sympy import prime
def a(x): return sum([prime(x + n) for n in range(9)])
print([a(i) for i in range(1, 50)]) # Indranil Ghosh, Mar 18 2017

a(n) = A127335(n)+A000040(n+8). - R. J. Mathar, Apr 24 2023

Edited by Klaus Brockhaus, Jan 13 2007

A127340 Primes that are the sum of 11 consecutive primes.

Original entry on oeis.org

233, 271, 311, 353, 443, 491, 631, 677, 883, 1367, 1423, 1483, 1543, 1607, 1787, 1901, 1951, 2011, 2141, 2203, 2383, 3253, 3469, 3541, 3617, 3691, 3967, 4159, 4229, 4297, 4943, 5009, 5483, 5657, 5741, 5903, 5981, 6553, 6871, 6991, 7057, 7121, 7187, 7873

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

Primes in A127338.

A prime number n is in the sequence if for some k it is the absolute value of coefficient of x^10 of the polynomial Prod_{j=0,10}(x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+10).

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

Cf. A127338, A034962, A034965, A082246, A082251, A127341.

a = {}; Do[If[PrimeQ[Sum[Prime[x + n], {n, 0, 10}]], AppendTo[a, Sum[Prime[x + n], {n, 0, 10}]]], {x, 1, 500}]; a
Select[Total/@Partition[Prime[Range[200]],11,1],PrimeQ] (* Harvey P. Dale, Jul 16 2012 *)

{m=125;k=11;for(n=0,m-1,a=sum(j=1,k,prime(n+j));if(isprime(a),print1(a,",")))} \\ Klaus Brockhaus, Jan 13 2007

{m=126;k=11;for(n=1,m,a=abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1));if(isprime(a),print1(a,",")))} \\ Klaus Brockhaus, Jan 13 2007

Edited by Klaus Brockhaus, Jan 13 2007

A127341 Primes that can be written as the sum of 13 consecutive primes.

Original entry on oeis.org

691, 863, 983, 1153, 1283, 1553, 1621, 1753, 1823, 2111, 2239, 2311, 2963, 3191, 3617, 3853, 4099, 4357, 4519, 4597, 4999, 5081, 5393, 5471, 5623, 5693, 5849, 6229, 6491, 6971, 7349, 7673, 8123, 8191, 8669, 8933, 9391, 10141, 10499, 10949, 11273

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

			691 = prime(10) + prime(11) + ... + prime(22) = 29 + 31 + ... + 79.

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

Cf. A034962, A034965, A082246, A082251, A127340.

Select[Table[Sum[Prime[i], {i, n, n + 12}], {n, 1, 150}], PrimeQ[ # ] &]
Select[Total/@Partition[Prime[Range[200]],13,1],PrimeQ] (* Harvey P. Dale, Aug 13 2021 *)

Edited by Stefan Steinerberger, Jul 31 2007

A127346 Primes in A127345.

Original entry on oeis.org

31, 71, 167, 311, 1151, 3119, 4871, 5711, 6791, 14831, 24071, 33911, 60167, 79031, 101159, 106367, 115631, 158231, 235751, 259751, 366791, 402551, 455471, 565919, 635711, 644951, 1124831, 1347971, 1510799, 1547927, 1743419, 1851671, 2048471

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

Primes of the form prime(k)*prime(k+1) + prime(k)*prime(k+2) + prime(k+1)*prime(k+2).

A prime number n is in the sequence if for some k it is the coefficient of x^1 of the polynomial Product_{j=0..2} (x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+2).

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

Cf. A127345, A127347, A127351, A006094, A002110, A034962, A034965, A082246, A082251, A127340, A127341, A070934, A046301, A046302, A046303, A046324, A046325, A046326, A046327.

b = {}; a = {}; Do[If[PrimeQ[Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[a, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[b, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]]], {x, 1, 100}]; Print[a] (* Artur Jasinski, Jan 11 2007 *)
s[li_] := li[[1]]*(li[[2]]+li[[3]])+li[[2]]*li[[3]]; Select[(s[#]&/@Partition[Prime[Range[100]], 3, 1]), PrimeQ] (* Zak Seidov, Jan 13 2012 *)

{m=143;k=2;for(n=1,m,a=sum(i=n,n+k-1,sum(j=i+1,n+k,prime(i)*prime(j)));if(isprime(a),print1(a,",")))} \\ Klaus Brockhaus, Jan 21 2007

{m=143;k=2;for(n=1,m,a=polcoeff(prod(j=0,k,(x-prime(n+j))),1);if(isprime(a),print1(a,",")))} \\ Klaus Brockhaus, Jan 21 2007

p=2; q=3; forprime(r=5, 1e3, if(isprime(t=p*q+p*r+q*r), print1(t", ")); p=q; q=r) \\ Charles R Greathouse IV, Jan 13 2012

a(n) = A127345(A204231(n)). - Zak Seidov, Jan 13 2012

Edited and extended by Klaus Brockhaus, Jan 21 2007

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...

A082252 Concatenation of (3n-2), (3n-1) and 3n divided by 3.

Original entry on oeis.org

41, 152, 263, 33704, 43805, 53906, 64007, 74108, 84209, 94310, 104411, 114512, 124613, 134714, 144815, 154916, 165017, 175118, 185219, 195320, 205421, 215522, 225623, 235724, 245825, 255926, 266027, 276128, 286229, 296330, 306431, 316532, 326633, 33367034

Offset: 1

Amarnath Murthy, Apr 11 2003

			a(5) = 131415/3 = 43805.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A082251, A082253, A082254, A082255, A082256.

a(n)={fromdigits(concat([digits(3*n-2), digits(3*n-1), digits(3*n)]))/3} \\ Andrew Howroyd, Nov 09 2019

Terms a(12) and beyond from Andrew Howroyd, Nov 09 2019

A082253 Concatenation of (5n-4), (5n-3), (5n-2), (5n-1) and 5n divided by 5.

Original entry on oeis.org

2469, 135782, 222426283, 323436384, 424446485, 525456586, 626466687, 727476788, 828486889, 929496990, 1030507091, 1131517192, 1232527293, 1333537394, 1434547495, 1535557596, 1636567697, 1737577798, 1838587899, 19395979820, 20220420620821, 21221421621822

Offset: 1

Amarnath Murthy, Apr 11 2003

			a(3) = 1112131415/5 = 222426283.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A082251, A082252, A082254, A082255, A082256.

a(n)={fromdigits(concat(vector(5, k, digits(5*(n-1)+k))))/5} \\ Andrew Howroyd, Nov 09 2019

Terms a(12) and beyond from Andrew Howroyd, Nov 09 2019

A082254 Concatenation of (6n-5), (6n-4), (6n-3), (6n-2), (6n-1) and 6n divided by 6.

Original entry on oeis.org

20576, 131516852, 21902526953, 32003537054, 42104547155, 52205557256, 62306567357, 72407577458, 82508587559, 92609597660, 102710607761, 112811617862, 122912627963, 133013638064, 143114648165, 153215658266, 163316516683517, 17184017517684518, 18185018518685519

Offset: 1

Amarnath Murthy, Apr 11 2003

			a(3) = 131415161718/6 = 21902526953.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A074996, A082251, A082252, A082253, A082255, A082256.

a(n)={fromdigits(concat(vector(6, k, digits(6*(n-1)+k))))/6} \\ Andrew Howroyd, Nov 09 2019

Terms a(8) and beyond from Andrew Howroyd, Nov 09 2019

cp's OEIS Frontend

A215991 Primes that are the sum of 25 consecutive primes.

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

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A127336 Numbers that are the sum of 9 consecutive primes.

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A127340 Primes that are the sum of 11 consecutive primes.

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A127341 Primes that can be written as the sum of 13 consecutive primes.

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A127346 Primes in A127345.

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

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