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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A234003 Prime(n), where n is such that (1+Sum_{i=1..n} prime(i)^5) / n is an integer.

Original entry on oeis.org

2, 3, 7, 13, 29, 37, 79, 271, 907, 2447, 3301, 4969, 9241, 26111, 27941, 38039, 58603, 90071, 243469, 617579, 849143, 6994363, 10661177, 68783413, 122137849, 131221879, 187987693, 194658539, 283102597, 329015387, 1682202323, 5230637117, 5461627177, 32315983207, 69900989237, 154638658121, 227225999443, 306462968363, 349585319959, 1128669425707, 1245067407509
Offset: 1

Views

Author

Robert Price, Dec 18 2013

Keywords

Comments

a(52) > 1005368767096627. - Bruce Garner, Jun 05 2021
a(53) > 4193009611262897. - Bruce Garner, Mar 28 2022

Examples

			a(4) = 13, because 13 is the 6th prime and the sum of the first 6 primes^5 + 1 = 552552 when divided by 6 equals 92092 which is an integer.

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

  • Mathematica
    t = {}; sm = 1; Do[sm = sm + Prime[n]^5; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
  • PARI
    is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^5); s==0 \\ Charles R Greathouse IV, Nov 30 2013

A234740 Sum of the eleventh powers of the first n primes.

Original entry on oeis.org

2048, 179195, 49007320, 2026334063, 287338004674, 2079498398711, 36351394706344, 152841653604563, 1105651411518490, 13306161177224319, 38714638073629150, 216632259853089563, 766961291569338004, 1696255031040560711, 4168414246124573014, 13437450175496764611
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A079395.

Programs

  • Mathematica
    Table[Sum[Prime[k]^11, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^11] (* This program is several hundred times faster than the first program, above, in calculating the first 1000 terms of the sequence. *) (* Harvey P. Dale, Sep 17 2023 *)
  • PARI
    s=[]; for(n=1, 15, s=concat(s, sum(i=1, n, prime(i)^11))); s \\ Colin Barker, Jan 20 2014

Formula

a(n) = Sum_{k=1..n} prime(k)^11.

A236209 Sum of the seventh powers of the first n primes.

Original entry on oeis.org

128, 2315, 80440, 903983, 20391154, 83139671, 493478344, 1387350083, 4792175530, 22042051839, 49554665950, 144486543083, 339240816964, 611059428071, 1117682548534, 2292393688371, 4781045173190, 7923788009211, 13984499614534, 23079619772925, 34127018292022
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A092759.

Programs

  • Mathematica
    Table[Sum[Prime[k]^7, {k, n}], {n, 1000}]

Formula

a(n) = Sum_{k=1..n} prime(k)^7.

A236214 Sum of the eighth powers of the first n primes.

Original entry on oeis.org

256, 6817, 397442, 6162243, 220521124, 1036251845, 8012009286, 24995572327, 103306557608, 603552970569, 1456444008010, 4968923461931, 12953848691052, 24642048968653, 48453335630414, 110713026041775, 257543463646096, 449250776643377, 855318454200018
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A179645.

Programs

  • Mathematica
    Table[Sum[Prime[k]^8, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^8] (* Harvey P. Dale, Feb 25 2016 *)

Formula

a(n) = Sum_{k=1..n} prime(k)^8.

A236215 Sum of the ninth powers of the first n primes.

Original entry on oeis.org

512, 20195, 1973320, 42326927, 2400274618, 13004773991, 131592650488, 454280348267, 2255433009730, 16762578985599, 43202201146270, 173163940941347, 500545875335308, 1003138487272151, 2122268960374918, 5422032552177051, 14085028370831990, 25779174463666131
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A179665.

Programs

  • Mathematica
    Table[Sum[Prime[k]^9, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^9] (* Harvey P. Dale, Jul 01 2015 *)

Formula

a(n) = Sum_{k=1..n} prime(k)^9.

A236216 Sum of the tenth powers of the first n primes.

Original entry on oeis.org

1024, 60073, 9825698, 292300947, 26229725548, 164088217397, 2180082117846, 8311148375647, 49737659589296, 470444892889497, 1290073179870298, 6098657552288147, 19521316862440548, 41132799175724797, 93731931411554846, 268619401777067895, 779736155077709296
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A030629.

Programs

  • Mathematica
    Table[Sum[Prime[k]^10, {k, n}], {n, 1000}]

Formula

a(n) = Sum_{k=1..n} prime(k)^10.

A236218 Sum of the twelfth powers of the first n primes.

Original entry on oeis.org

4096, 535537, 244676162, 14085963363, 3152514340084, 26450599462565, 609072836692326, 2822387755758487, 24737012187778808, 378551795393247849, 1166214579181797610, 7749166585021832891, 30312656885388018972, 70272287682650595373, 186463770791599173614
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A030631.

Programs

  • Mathematica
    Table[Sum[Prime[k]^12, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^12] (* Harvey P. Dale, Jan 31 2014 *)
  • PARI
    s=[]; for(n=1, 15, s=concat(s, sum(i=1, n, prime(i)^12))); s \\ Colin Barker, Jan 20 2014

Formula

a(n) = sum(k = 1 .. n, prime(k)^12).

A236221 Sum of the thirteenth powers of the first n primes.

Original entry on oeis.org

8192, 1602515, 1222305640, 98111316047, 34620823459978, 337495930052231, 10242073962958168, 52295057425215227, 556331419361682610, 10816960132320284799, 35234506429765327390, 278803730645846632787, 1203906832960860262108, 2922170957243151047351
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
Partial sums of A138031.

Programs

  • Mathematica
    Table[Sum[Prime[k]^13, {k, n}], {n, 100}]

Formula

a(n) = Sum_{k=1..n} prime(k)^13.

A236222 Sum of the fourteenth powers of the first n primes.

Original entry on oeis.org

16384, 4799353, 6108314978, 684331387827, 380434164971068, 4317810550670357, 172695637110071286, 971702322892955407, 12564538647431705216, 310122771323231168697, 1067066706544027489018, 10079128002539035788707, 48008355197454594590868
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

  • Mathematica
    Table[Sum[Prime[k]^14, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^14] (* Harvey P. Dale, Nov 26 2014 *)

Formula

a(n) = sum(k = 1 .. n, prime(k)^14).

A236223 Sum of the fifteenth powers of the first n primes.

Original entry on oeis.org

32768, 14381675, 30531959800, 4778093469743, 4182026262885394, 55367919276976151, 2917790970786791944, 18098918000661590243, 284734153465052835850, 8913922901063237276799, 32379184892907923206750, 365825452844723230295243, 1920923767836261141183844
Offset: 1

Views

Author

Robert Price, Jan 20 2014

Keywords

Links

Crossrefs

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

  • Mathematica
    Table[Sum[Prime[k]^15, {k, n}], {n, 1000}]
Accumulate[Prime[Range[15]]^15] (* Harvey P. Dale, Mar 09 2022 *)

Formula

a(n) = sum(k = 1 .. n, prime(k)^15).
Previous Showing 71-80 of 93 results. Next

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