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 13 results. Next

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

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

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

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

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

A133559 Primes which have a partition as the sum of squares of five consecutive primes.

Original entry on oeis.org

373, 653, 5381, 6701, 8069, 19541, 24821, 53549, 56909, 69389, 93581, 107741, 131837, 184901, 196661, 237821, 252509, 344021, 370661, 395069, 498989, 609269, 783701, 1055429, 1174781, 1239341, 1492637, 1576229, 1713989, 1749149, 2024261
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Comments

For sums of squares of two consecutive primes, only 2^2 + 3^2 = 13 is prime.
For sums of squares of three consecutive primes (A133529), it seems that only 83 belonging (checked for starting primes prime(k) for all k < 1000000).
Sums of squares of four (and all even numbers of) consecutive primes are even numbers with the exception of 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.

Examples

			a(1)=373 because prime(2)^2 + prime(3)^2 + prime(4)^2 + prime(5)^2 + prime(6)^2 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373 is prime. [Corrected by _Jonathan Sondow_, Nov 04 2015]

Links

Crossrefs

Cf. A133529, A133538, A133560.

Programs

  • Mathematica
    b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
Select[Total/@Partition[Prime[Range[200]]^2,5,1],PrimeQ] (* Harvey P. Dale, Apr 07 2015 *)

A133541 Sum of fifth powers of five consecutive primes.

Original entry on oeis.org

181258, 552519, 1972133, 4445107, 10864643, 31214741, 59472599, 127396699, 240776801, 381348901, 590182759, 979749101, 1625329443, 2354069543, 3557186207, 5132070551, 6786946651, 9149078751, 12243523093, 16477457435
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=181258 because 2^5+3^5+5^5+7^5+11^5=181258.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537, A034964, A133538, A133539, A133540, A133542, A133543.

Programs

  • Mathematica
    a = 5; 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[30]]^5,5,1] (* Harvey P. Dale, Dec 02 2017 *)

Formula

a(n) = A133527(n) + A050997(n+4). - Michel Marcus, Nov 09 2013

A133542 Sum of sixth powers of five consecutive primes.

Original entry on oeis.org

1905628, 6732373, 30869213, 77899469, 225817709, 818869469, 1701546341, 4243135181, 8946193541, 15119520701, 25303912709, 46580770157, 86195577389, 132965847509, 217102866629, 334423935221, 463593800381, 664500722261
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=1905628 because 2^6+3^6+5^6+7^6+11^6=1905628.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537, A034964, A133538, A133539, A133540, A133541, A133543.

Programs

  • Mathematica
    a = 6; 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[30]],5,1]^6)  (* Harvey P. Dale, Mar 13 2011 *)

Formula

a(n) = A133528(n) + A030516(n+4). - Michel Marcus, Nov 09 2013

A133560 Primes which have a partition as the sum of squares of seven consecutive primes.

Original entry on oeis.org

1543, 3271, 4519, 7591, 9439, 11719, 23599, 39631, 45319, 51031, 56599, 90199, 151471, 173359, 210319, 222919, 235159, 261463, 313879, 367711, 402511, 459223, 478831, 499711, 610567, 634327, 732967, 760519, 819319, 883087, 939439, 968959
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Comments

For sums of squares of two consecutive primes, only 2^2 + 3^2 = 13 is prime.
For sums of squares of three consecutive primes (see A133529), it seems that only 3^2 + 5^2 + 7^2 = 83 is prime.
Sums of squares of four (and all even numbers of) consecutive primes are even numbers except for 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.
For sums of squares of five of consecutive primes see A133559.
For every prime p > 3, p^2 mod 3 = 1, so the sum of the squares of any 3 such primes will be divisible by 3. - Jon E. Schoenfield, Sep 04 2023

Examples

			a(3)=4519 because 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519 is prime.

Links

Crossrefs

Cf. A133529, A133538, A133559, A133561.

Programs

  • Maple
    select(isprime,[seq(add(ithprime(n+k)^2,k=0..6),n=1..80)]); # Muniru A Asiru, Jul 19 2018
  • Mathematica
    b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a + Prime[n + 5]^a + Prime[n + 6]^a; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
(* Second program: *)
Select[Map[Total, Partition[Prime@ Range@ 80, 7, 1]^2], PrimeQ] (* Michael De Vlieger, Jul 20 2018 *)
Showing 1-10 of 13 results. Next

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