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.

Showing 1-10 of 31 results. Next

A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529).

Original entry on oeis.org

83, 366819, 1055019, 1947411, 2740107, 3694179, 6627579, 8851251, 9430899, 20243811, 28391619, 37545291, 38242083, 49459179, 56550291, 88205211, 101931891, 103429491, 108060339, 135085851, 176962659, 183973851, 194907051, 196911171, 212874531, 249687699, 271986651
Offset: 1

Views

Author

Zak Seidov, May 29 2017

Keywords

Comments

The only prime number is 83.

Examples

			83=A034961(9)=A133529(2),
366819=A034961(11502)=A133529(69),
1055019=A034961(30105)=A133529(107),
1947411=A034961(52758)=A133529(139),
2740107=A034961(72260)=A133529(161),
3694179=A034961(95152)=A133529(185).

Links

Crossrefs

Cf. A034961 Sums of three consecutive primes. A133529 Sum of squares of three consecutive primes.

Programs

  • Python
    from _future_ import division
from sympy import prevprime, nextprime, isprime
A287686_list, p2, q2, r2, r = [], 4, 9, 25, 5
while r < 10**6:
    n = p2+q2+r2
    m = n//3
    pm, nm = prevprime(m), nextprime(m)
    k = n - pm - nm
    if isprime(m):
        if m == k:
            A287686_list.append(n)
    else:
        if nextprime(nm) == k or prevprime(pm) == k:
            A287686_list.append(n)
    s = nextprime(r)
    p2, q2, r2, r = q2, r2, s**2, s # Chai Wah Wu, May 30 2017

A133524 Sum of squares of four consecutive primes.

Original entry on oeis.org

87, 204, 364, 628, 940, 1348, 2020, 2692, 3700, 4852, 5860, 7108, 8548, 10348, 12220, 14500, 16732, 18580, 21100, 23500, 26380, 30460, 34420, 38140, 41668, 44140, 46708, 52228, 57940, 64828, 71380, 77452, 83092, 88972, 96220, 101908, 109036
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=87 because 2^2+3^2+5^2+7^2=87.

Links

Crossrefs

Cf. A034963.

Programs

  • Mathematica
    a = 2; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[40]]^2,4,1] (* Harvey P. Dale, Dec 09 2018 *)
  • PARI
    a(n)=sum(i=n, n+3, prime(i)^2) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = A133529(n) + A001248(n+3). - Michel Marcus, Nov 08 2013
a(n) ~ 4n^2 log^2 n. - Charles R Greathouse IV, Apr 29 2015

A133530 Sum of third powers of three consecutive primes.

Original entry on oeis.org

160, 495, 1799, 3871, 8441, 13969, 23939, 43415, 66347, 104833, 149365, 199081, 252251, 332207, 458079, 581237, 733123, 885655, 1047691, 1239967, 1453843, 1769795, 2189429, 2647943, 3035701, 3348071, 3612799, 3962969, 4786309
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=160 because 2^3+3^3+5^3=160.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133531, A133532, A133533.

Programs

  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133534(n) + A030078(n+2). - Michel Marcus, Nov 08 2013

A133531 Sum of fourth powers of three consecutive primes.

Original entry on oeis.org

722, 3107, 17667, 45603, 126723, 242403, 493683, 1117443, 1910643, 3504963, 5623443, 8118723, 11124243, 16188963, 24887523, 33853683, 46114323, 59408643, 73961043, 92760003, 114806643, 149150643, 198729843, 255331923, 305140563
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=722 because 2^4+3^4+5^4=722.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133532, A133533.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133535(n) + A030514(n+2). - Michel Marcus, Nov 09 2013

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

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

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

A133537 Sum of sixth powers of two consecutive primes.

Original entry on oeis.org

793, 16354, 133274, 1889210, 6598370, 28964378, 71183450, 195081770, 742859210, 1482327002, 3453230090, 7315830650, 11071467290, 17100578378, 32943576458, 64344894770, 93700908002, 141978756530, 218558666090, 279434510210
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=793 because 2^6+3^6=793.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133538.

Programs

  • Mathematica
    a = 6; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]

Formula

a(n) = A030516(n) + A030516(n+1). - Michel Marcus, Nov 09 2013
Showing 1-10 of 31 results. Next

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