A034964 -id:A034964 - cp's OEIS frontend

A034965 Primes that are sum of five consecutive primes.

53, 67, 83, 101, 139, 181, 199, 263, 311, 331, 373, 421, 449, 587, 617, 647, 683, 733, 787, 811, 839, 863, 941, 991, 1123, 1151, 1193, 1361, 1381, 1579, 1609, 1801, 1831, 1861, 1949, 1979, 2081, 2113, 2143, 2221, 2273, 2297, 2357, 2423, 2459, 2689, 2731

Offset: 1

Patrick De Geest, Oct 15 1998

nonn

			53 = 5 + 7 + 11 + 13 + 17.
373 = 67 + 71 + 73 + 79 + 83.

Harvey P. Dale and Syed Iddi Hasan, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A001043, A011974, A034707, A152468. Also Cf. A034964, of which this sequence is a subset.

ts_prod_n:=proc(n) local i,ans; ans:=[ ]: for i from 1 to n do if isprime(ithprime(i)+ithprime(i+1)+ithprime(i+2)+ithprime(i+3)+ithprime(i+4))= 'true' then ans:=[op(ans), ithprime(i)+ithprime(i+1)+ithprime(i+2)+ithprime(i+3)+ithprime(i+4) ]: fi od: end: ts_prod_n(701); # Jani Melik, May 05 2006

Select[Table[Plus@@Prime[Range[n, n + 4]], {n, 200}], PrimeQ] (* Alonso del Arte, Dec 30 2011 *)
Select[Total/@Partition[Prime[Range[200]],5,1],PrimeQ] (* Harvey P. Dale, May 24 2012 *)

Corrected example by Paul S. Coombes, Dec 29 2011

A127337 Numbers that are the sum of 10 consecutive primes.

Original entry on oeis.org

129, 158, 192, 228, 264, 300, 340, 382, 424, 468, 510, 552, 594, 636, 682, 732, 780, 824, 870, 912, 954, 1008, 1060, 1114, 1164, 1216, 1266, 1320, 1376, 1434, 1494, 1546, 1596, 1650, 1704, 1752, 1800, 1854, 1914, 1974, 2030, 2084, 2142, 2192, 2250, 2310, 2374

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) is the absolute value of coefficient of x^9 of the polynomial Product_{j=0..9} (x - prime(n+j)) of degree 10; the roots of this polynomial are prime(n), ..., prime(n+9).

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

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127338, A127339.

[&+[ NthPrime(n+k): k in [0..9] ]: n in [1..90] ]; // Vincenzo Librandi, Apr 03 2011

A127337 := proc(n)
    local i ;
    add(ithprime(n+i),i=0..9) ;
end proc:
seq(A127337(n),n=1..30) ; # R. J. Mathar, Apr 24 2023

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a
Table[Plus@@Prime[Range[n, n + 9]], {n, 50}] (* Alonso del Arte, Feb 15 2011 *)
ListConvolve[ConstantArray[1, 10], Prime[Range[50]]]
Total/@Partition[Prime[Range[60]],10,1] (* Harvey P. Dale, Jan 31 2013 *)

{m=46;k=10;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

{m=46;k=10;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(n): return sum(prime(n + i) for i in range(10))
print([a(n) for n in range(1, 48)]) # Michael S. Branicky, Dec 09 2021

# faster version for generating initial segment of sequence
from sympy import nextprime
def aupton(terms):
    alst, plst = [], [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
    for n in range(terms):
        alst.append(sum(plst))
        plst = plst[1:] + [nextprime(plst[-1])]
    return alst
print(aupton(47)) # Michael S. Branicky, Dec 09 2021

a(n) = A127336(n)+A000040(n+9). - R. J. Mathar, Apr 24 2023

Edited by Klaus Brockhaus, Jan 13 2007

A127333 Numbers that are the sum of 6 consecutive primes.

Original entry on oeis.org

41, 56, 72, 90, 112, 132, 156, 180, 204, 228, 252, 280, 304, 330, 358, 384, 410, 434, 462, 492, 522, 552, 580, 606, 630, 660, 690, 724, 756, 796, 834, 864, 896, 926, 960, 990, 1020, 1054, 1084, 1114, 1140, 1172, 1214, 1250, 1286, 1322, 1362, 1392, 1420

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) is the absolute value of coefficient of x^5 of the polynomial Prod_{j=0,5}(x-prime(n+j)) of degree 6; the zeros of this polynomial are prime(n), ..., prime(n+5).

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

Cf. A011974, A001043, A034961, A034963, A034964, A127334, A127335, A127336, A127337, A127338, A127339.

[&+[ NthPrime(n+k): k in [0..5] ]: n in [1..80] ]; /* Vincenzo Librandi, Apr 03 2011 */

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 5}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],6,1] (* Harvey P. Dale, Mar 12 2015 *)

{m=50;k=6;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 12 2007

{m=50;k=6;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 12 2007

Edited by Klaus Brockhaus, Jan 12 2007

A127335 Numbers that are the sum of 8 successive primes.

Original entry on oeis.org

77, 98, 124, 150, 180, 210, 240, 270, 304, 340, 372, 408, 442, 474, 510, 546, 582, 620, 660, 696, 732, 768, 802, 846, 888, 928, 966, 1012, 1056, 1104, 1154, 1194, 1236, 1278, 1320, 1362, 1404, 1444, 1480, 1524, 1574, 1622, 1670, 1712, 1758, 1802, 1854, 1900

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) is the absolute value of coefficient of x^7 of the polynomial Prod_{j=0,7}(x-prime(n+j)) of degree 8; the roots of this polynomial are prime(n), ..., prime(n+7).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127336, A127337, A127338, A127339.

[&+[ NthPrime(n+k): k in [0..7] ]: n in [1..90] ]; // Vincenzo Librandi, Apr 03 2011

S:= [0,op(ListTools:-PartialSums(select(isprime, [2,seq(i,i=3..1000,2)])))]:
S[9..-1]-S[1..-9]; # Robert Israel, Nov 27 2017

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 7}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],8,1] (* Harvey P. Dale, Sep 10 2019 *)

{m=48;k=8;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

{m=48;k=8;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 13 2007

a(n)=my(p=prime(n));p+sum(i=2,8,p=nextprime(p+1)) \\ Charles R Greathouse IV, Apr 19 2015

a(n) ~ 8n log n. - Charles R Greathouse IV, Apr 19 2015

Edited by Klaus Brockhaus, Jan 13 2007

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

A127338 Numbers that are the sum of 11 consecutive primes.

Original entry on oeis.org

160, 195, 233, 271, 311, 353, 399, 443, 491, 539, 583, 631, 677, 725, 779, 833, 883, 931, 979, 1025, 1081, 1139, 1197, 1253, 1313, 1367, 1423, 1483, 1543, 1607, 1673, 1727, 1787, 1843, 1901, 1951, 2011, 2077, 2141, 2203, 2263, 2323, 2383, 2443, 2507

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) = absolute value of coefficient of x^10 of the polynomial Product_{j=0..10} (x - prime(n+j)) of degree 11; the roots of this polynomial are prime(n), ..., prime(n+10).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127339, A127340.

[&+[ NthPrime(n+k): k in [0..10] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011

f[n_] := Sum[Prime[n + i], {i, 0, 10}]; Array[f, 45]
Plus @@@ Partition[ Prime@ Range@ 55, 11, 1] (* Robert G. Wilson v, Jan 13 2011 *)

{m=45;k=11;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

{m=45;k=11;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 13 2007

Edited by Klaus Brockhaus, Jan 13 2007

A127334 Numbers that are the sum of 7 consecutive primes.

Original entry on oeis.org

58, 75, 95, 119, 143, 169, 197, 223, 251, 281, 311, 341, 371, 401, 431, 463, 493, 523, 559, 593, 625, 659, 689, 719, 757, 791, 827, 863, 905, 947, 991, 1027, 1063, 1099, 1139, 1171, 1211, 1247, 1281, 1313, 1351, 1395, 1441, 1479, 1519, 1561, 1603, 1643

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) = absolute value of coefficient of x^6 of the polynomial Product_{j=0..6} (x - prime(n+j)) of degree 7; the roots of this polynomial are prime(n), ..., prime(n+6).

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Cf. A001043, A011974, A034961, A034963, A034964, A082246, A127333, A127335, A127336, A127337, A127338, A127339.

P:=Filtered([1..1000],IsPrime);; List([0..50],n->Sum([1+n..7+n],i->P[i])); # Muniru A Asiru, Apr 16 2018

[&+[ NthPrime(n+k): k in [0..6] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011

seq(add(ithprime(i),i=n..6+n),n=1..50); # Muniru A Asiru, Apr 16 2018

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 6}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],7,1] (* Harvey P. Dale, May 14 2023 *)

{m=48;k=7;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

{m=48;k=7;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(7))
print([a(i) for i in range(1, 50)]) # Indranil Ghosh, Mar 18 2017

BB = primes_first_n(62)
L = []
for i in range(55):
    L.append(sum(BB[i+j] for j in range(7)))
L
# Zerinvary Lajos, May 14 2007

Edited by Klaus Brockhaus, Jan 13 2007

A127339 Numbers that are the sum of 12 consecutive primes.

Original entry on oeis.org

197, 236, 276, 318, 364, 412, 460, 510, 562, 612, 662, 714, 766, 822, 880, 936, 990, 1040, 1092, 1152, 1212, 1276, 1336, 1402, 1464, 1524, 1586, 1650, 1716, 1786, 1854, 1918, 1980, 2040, 2100, 2162, 2234, 2304, 2370, 2436, 2502, 2564, 2634, 2700, 2770

Offset: 1

Artur Jasinski, Jan 11 2007

nonn

a(n) = absolute value of coefficient of x^11 of the polynomial Product_{j=0..11} (x - prime(n+j)) of degree 12; the roots of this polynomial are prime(n), ..., prime(n+11).

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127338.

[&+[ NthPrime(n+k): k in [0..11] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 11}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],12,1] (* Harvey P. Dale, May 05 2018 *)

{m=45;k=12;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

{m=45;k=12;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 13 2007

Edited by Klaus Brockhaus, Jan 13 2007

A133539 Sum of third powers of five consecutive primes.

Original entry on oeis.org

1834, 4023, 8909, 15643, 27467, 50525, 78119, 123859, 185921, 253261, 332695, 451781, 606507, 764567, 985823, 1239911, 1480051, 1767711, 2112517, 2516723, 3071485, 3712769, 4312457, 4965713, 5555773, 6085997, 7104079, 8259443

Offset: 1

Artur Jasinski, Sep 14 2007

nonn

			a(1)=1834 because 2^3+3^3+5^3+7^3+11^3=1834.

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537, A034964, A133538, A133540, A133541, A133542, A133543.

a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total[#^3]&/@Partition[Prime[Range[40]],5,1] (* Harvey P. Dale, May 01 2013 *)

a(n) = A133525(n) + A030078(n+4). - Michel Marcus, Nov 09 2013

A133543 Sum of seventh powers of five consecutive primes.

Original entry on oeis.org

20391154, 83139543, 493476029, 1387269643, 4791271547, 22021660685, 49471526279, 143993064739, 337853466881, 606267252541, 1095640496695, 2242839022421, 4636558630107, 7584547192247, 13373440186463

Offset: 1

Artur Jasinski, Sep 14 2007

nonn

			a(1)=20391154 because 2^7+3^7+5^7+7^7+11^7=20391154

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

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537, A034964, A133538, A133539, A133540, A133541, A133542.

a = 7; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[20]]^7,5,1] (* Harvey P. Dale, Mar 05 2022 *)

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A034965 Primes that are sum of five consecutive primes.

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A127337 Numbers that are the sum of 10 consecutive primes.

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A127333 Numbers that are the sum of 6 consecutive primes.

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A127335 Numbers that are the sum of 8 successive primes.

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A127336 Numbers that are the sum of 9 consecutive primes.

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A127338 Numbers that are the sum of 11 consecutive primes.

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