cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A133532 Sum of fifth powers of three consecutive primes.

Original entry on oeis.org

3400, 20175, 180983, 549151, 1952201, 4267249, 10332299, 29423591, 55576643, 118484257, 213829309, 332208601, 492209651, 794548943, 1362464799, 1977716093, 2909645707, 3998950759, 5227426051, 6954357343, 9089168635
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=3400 because 2^5+3^5+5^5=3400.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133533.

Programs

  • Mathematica
    a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total[#^5]&/@Partition[Prime[Range[30]],3,1] (* Harvey P. Dale, May 26 2011 *)

Formula

a(n) = A133536(n) + A050997(n+2). - Michel Marcus, Nov 09 2013

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

Views

Author

Artur Jasinski, Jan 11 2007

Keywords

Comments

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).

Links

Crossrefs

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

Programs

  • Magma
    [&+[ NthPrime(n+k): k in [0..5] ]: n in [1..80] ]; /* Vincenzo Librandi, Apr 03 2011 */
  • Mathematica
    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 *)
  • PARI
    {m=50;k=6;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 12 2007
  • PARI
    {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

Extensions

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

Views

Author

Artur Jasinski, Jan 11 2007

Keywords

Comments

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).

Links

Crossrefs

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

Programs

  • Magma
    [&+[ NthPrime(n+k): k in [0..7] ]: n in [1..90] ]; // Vincenzo Librandi, Apr 03 2011
  • Maple
    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
  • Mathematica
    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 *)
  • PARI
    {m=48;k=8;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007
  • PARI
    {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
  • PARI
    a(n)=my(p=prime(n));p+sum(i=2,8,p=nextprime(p+1)) \\ Charles R Greathouse IV, Apr 19 2015

Formula

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

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

A133538 Sum of seventh powers of two consecutive primes.

Original entry on oeis.org

2315, 80312, 901668, 20310714, 82235688, 473087190, 1304210412, 4298697186, 20654701756, 44762490420, 122444491244, 289686151014, 466572884988, 778441731570, 1681334260300, 3663362624656, 5631394320840, 9203454441344, 15155831763714, 20142518677488
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=2315 because 2^7 + 3^7 = 2315.

Links

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537.

Programs

  • Magma
    [NthPrime(n)^7 + NthPrime(n+1)^7: n in [1..25]]; // Vincenzo Librandi, Aug 23 2018
  • Maple
    seq(add(ithprime(n+k)^7,k=0..1),n=1..20); # Muniru A Asiru, Aug 22 2018
  • Mathematica
    e = 7; Table[Prime[n]^e + Prime[n + 1]^e, {n, 1, 100}]
Total/@Partition[Prime[Range[20]]^7,2,1] (* Harvey P. Dale, Oct 16 2014 *)
  • PARI
    a(n) = prime(n)^7 + prime(n+1)^7; \\ Michel Marcus, Aug 22 2018

Formula

a(n) = A092759(n) + A092759(n+1). - Michel Marcus, Nov 09 2013

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

Views

Author

Artur Jasinski, Jan 11 2007

Keywords

Comments

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).

Crossrefs

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

Programs

  • Magma
    [&+[ NthPrime(n+k): k in [0..8] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011
  • Mathematica
    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 *)
  • PARI
    {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
  • Python
    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

Formula

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

Extensions

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

Views

Author

Artur Jasinski, Jan 11 2007

Keywords

Comments

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).

Links

Crossrefs

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

Programs

  • Magma
    [&+[ NthPrime(n+k): k in [0..10] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011
  • Mathematica
    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 *)
  • PARI
    {m=45;k=11;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007
  • PARI
    {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

Extensions

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

Views

Author

Artur Jasinski, Jan 11 2007

Keywords

Comments

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).

Links

Crossrefs

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

Programs

  • GAP
    P:=Filtered([1..1000],IsPrime);; List([0..50],n->Sum([1+n..7+n],i->P[i])); # Muniru A Asiru, Apr 16 2018
  • Magma
    [&+[ NthPrime(n+k): k in [0..6] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011
  • Maple
    seq(add(ithprime(i),i=n..6+n),n=1..50); # Muniru A Asiru, Apr 16 2018
  • Mathematica
    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 *)
  • PARI
    {m=48;k=7;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007
  • PARI
    {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
  • Python
    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
  • Sage
    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

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

A133534 Sum of third powers of two consecutive primes.

Original entry on oeis.org

35, 152, 468, 1674, 3528, 7110, 11772, 19026, 36556, 54180, 80444, 119574, 148428, 183330, 252700, 354256, 432360, 527744, 658674, 746928, 882056, 1064826, 1276756, 1617642, 1942974, 2123028, 2317770, 2520072, 2737926, 3491280
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=35 because 2^3+3^3=35.

Links

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133535, A133536, A133537, A133538.

Programs

  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
Total[#^3]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 29 2021 *)

Formula

a(n) = A030078(n) + A030078(n+1). - Michel Marcus, Nov 09 2013

A133535 Sum of fourth powers of two consecutive primes.

Original entry on oeis.org

97, 706, 3026, 17042, 43202, 112082, 213842, 410162, 987122, 1630802, 2797682, 4699922, 6244562, 8298482, 12770162, 20007842, 25963202, 33996962, 45562802, 53809922, 67348322, 86408402, 110200562, 151271522, 192589682, 216611282
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=2^4+3^4=97.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133536, A133537, A133538.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]

Formula

a(n) = A030514(n) + A030514(n+1). - Michel Marcus, Nov 09 2013

A133536 Sum of fifth powers of two consecutive primes.

Original entry on oeis.org

275, 3368, 19932, 177858, 532344, 1791150, 3895956, 8912442, 26947492, 49140300, 97973108, 185200158, 262864644, 376353450, 647540500, 1133119792, 1559520600, 2194721408, 3154354458, 3877300944, 5150127992, 7016097042, 9523100092
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=2^5+3^5=275.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133537, A133538.

Programs

  • Mathematica
    a = 5; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]

Formula

a(n) = A050997(n) + A050997(n+1). - Michel Marcus, Nov 09 2013
Previous Showing 11-20 of 47 results. Next

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