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 12 results. Next

A232823 Numbers k such that k divides 1 + Sum_{j=1..k} (prime(j)^8).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 24, 28, 30, 32, 37, 39, 40, 45, 48, 60, 64, 80, 90, 96, 100, 104, 120, 133, 160, 168, 174, 180, 205, 211, 240, 247, 320, 360, 456, 480, 512, 540, 560, 563, 580, 676, 692, 735, 820, 864, 930, 960, 1215, 1216, 1368
Offset: 1

Views

Author

Robert Price, Nov 30 2013

Keywords

Comments

a(305) > 1.2*10^14. - Bruce Garner, Mar 20 2022

Examples

			a(7)=8 because 1 plus the sum of the first 8 primes^8 is 24995572328 which is divisible by 8.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 521330000, s = s + p^8; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p](* Derived from A128169 *)
With[{nn=1400},Select[Thread[{Range[nn],Accumulate[Prime[Range[nn]]^8]+1}],Mod[ #[[2]],#[[1]]] == 0&]][[;;,1]] (* Harvey P. Dale, Jul 20 2024 *)

A232964 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^9.

Original entry on oeis.org

1, 2, 4, 6, 10, 12, 14, 82, 93, 476, 712, 856, 935, 11104, 11706, 12234, 19500, 21490, 31864, 171252, 628863, 10189718, 12363588, 13976077, 22321041, 36642393, 47563206, 102352700, 869166585, 1197804361, 1400403575, 2199080290, 5225532140, 39957170689
Offset: 1

Views

Author

Robert Price, Dec 02 2013

Keywords

Comments

a(49) > 3*10^13. - Bruce Garner, Jun 05 2021

Examples

			a(5)=10 because 1 plus the sum of the first 10 primes^9 is 16762578985600 which is divisible by 10.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^9; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

A232966 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^14.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 13, 24, 26, 28, 45, 48, 88, 168, 360, 474, 540, 550, 864, 1104, 1230, 1408, 1488, 1816, 2367, 2677, 3507, 5592, 5916, 6612, 11238, 12925, 14124, 23523, 24087, 27356, 41528, 43465, 56951, 74688, 79244, 86682, 181730, 186136, 193704
Offset: 1

Views

Author

Robert Price, Dec 02 2013

Keywords

Comments

a(120) > 2*10^13. - Bruce Garner, Jun 02 2021

Examples

			a(7)=9 because 1 plus the sum of the first 9 primes^14 is 12564538647431705217 which is divisible by 9.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^14; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

A233133 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^10.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 22, 24, 26, 27, 33, 44, 45, 48, 66, 71, 76, 88, 107, 132, 148, 168, 176, 187, 207, 216, 264, 330, 360, 418, 440, 462, 528, 672, 864, 880, 1056, 1221, 1276, 1304, 1340, 1408, 1465, 1531, 1672, 1683, 2153, 2374, 2760, 3520
Offset: 1

Views

Author

Robert Price, Dec 04 2013

Keywords

Comments

a(211) > 3.0*10^13. - Bruce Garner, Jun 06 2021

Examples

			a(5)=6 because 1 plus the sum of the first 6 primes^10 is 164088217398 which is divisible by 6.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^10; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
Module[{nn=3600,sp},sp=Accumulate[Prime[Range[nn]]^10];Select[ Range[ nn],Divisible[ sp[[#]]+1,#]&]] (* Harvey P. Dale, Sep 18 2018 *)

A233193 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^11.

Original entry on oeis.org

1, 2, 4, 5, 6, 10, 12, 17, 22, 45, 87, 217, 546, 17806, 41850, 127973, 189586, 435067, 475810, 595932, 3319478, 3737221, 5741156, 7349730, 7473734, 13114674, 26076896, 48515830, 48791555, 419983404, 2217443166, 2617207503, 2894318150, 8776851351, 118596802796
Offset: 1

Views

Author

Robert Price, Dec 05 2013

Keywords

Comments

a(47) > 3*10^13. - Bruce Garner, Jun 05 2021

Examples

			a(5)=6 because 1 plus the sum of the first 6 primes^11 is 2079498398712  which is divisible by 6.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^11; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
With[{nn = 5*10^7},Select[Thread[{Accumulate[ Prime[ Range[nn]]^11] + 1, Range[nn]}], Divisible[#[[1]], #[[2]]] &][[All, 2]]] (* The program generates the first 29 terms of the sequence. To generate all 34, change the value of nn to 878*10^7, but the program will take a long time to run. *) (* Harvey P. Dale, Mar 09 2017 *)

Extensions

a(35) from Karl-Heinz Hofmann, Mar 07 2021

A233264 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^12.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 24, 26, 27, 28, 30, 35, 36, 39, 40, 42, 45, 46, 48, 52, 54, 56, 60, 63, 65, 66, 70, 72, 78, 80, 84, 87, 90, 91, 100, 104, 105, 112, 117, 120, 126, 130, 138, 140, 144, 154, 156, 160, 168, 175, 176
Offset: 1

Views

Author

Robert Price, Dec 06 2013

Keywords

Comments

a(1171) > 2*10^13. - Bruce Garner, Jun 06 2021

Examples

			5 is a term because 1 plus the sum of the first 11 primes^12 is 3152514340085 which is divisible by 11.

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

  • Maple
    A233264:=n->if type((1+add(ithprime(i)^12, i=1..n))/n, integer) then n; fi; seq(A233264(n), n=1..200); # Wesley Ivan Hurt, Dec 06 2013
  • Mathematica
    p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^12; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
With[{nn=200},Transpose[Select[Thread[{Accumulate[Prime[Range[nn]]^12], Range[nn]}], Divisible[#[[1]]+1,#[[2]]]&]][[2]]] (* Harvey P. Dale, May 28 2015 *)

A233349 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^13.

Original entry on oeis.org

1, 2, 4, 6, 10, 12, 52, 74, 136, 242, 305, 670, 1431, 1706, 1713, 3956, 18331, 22238, 25162, 107332, 162778, 169479, 431228, 459704, 1808681, 1813273, 5954563, 10351930, 27931668, 32490143, 201039164, 311357190, 733854046, 1677164490, 3722808264, 9000784596
Offset: 1

Views

Author

Robert Price, Dec 07 2013

Keywords

Comments

a(47) > 1.4*10^13. - Bruce Garner, May 05 2021

Examples

			a(5) = 10 because 1 plus the sum of the first 10 primes^13 is 10816960132320284800 which is divisible by 10.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^13; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

A233413 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^15.

Original entry on oeis.org

1, 2, 4, 5, 6, 10, 12, 14, 22, 74, 397, 524, 620, 857, 3727, 8171, 9194, 41032, 59604, 109471, 123231, 166394, 195736, 203440, 494620, 805738, 3000362, 6861264, 64286003, 69417562, 113888084, 162292604, 241184820, 658646484, 864667379, 1027008032, 4023976348
Offset: 1

Views

Author

Robert Price, Dec 09 2013

Keywords

Comments

a(49) > 2*10^13. - Bruce Garner, Jun 02 2021

Examples

			a(6)=10 because 1 plus the sum of the first 10 primes^15 is 8913922901063237276800 which is divisible by 10.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^15; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

A233461 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^16.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 20, 24, 27, 30, 32, 34, 39, 40, 45, 48, 51, 55, 57, 60, 64, 68, 80, 85, 90, 96, 100, 102, 120, 128, 136, 160, 168, 170, 180, 186, 192, 204, 205, 216, 230, 238, 240, 255, 272, 285, 320, 340, 360, 384, 408, 480, 510
Offset: 1

Views

Author

Robert Price, Dec 10 2013

Keywords

Comments

a(616) > 1.5*10^13. - Bruce Garner, Jun 06 2021

Examples

			a(9)=10 because 1 plus the sum of the first 10 primes^16 is 256716898101196243797130 which is divisible by 10.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^16; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

A233556 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^17.

Original entry on oeis.org

1, 2, 4, 6, 10, 12, 116, 147, 324, 2070, 2902, 3663, 4994, 11531, 13554, 22421, 558905, 1242890, 1655487, 2021278, 2878297, 4790338, 7061177, 16875261, 21813642, 24563860, 58919808, 69676102, 85356321, 92610708, 205600836, 338430087, 343675600, 1176903461, 1698127637, 4657254361, 17421656611
Offset: 1

Views

Author

Robert Price, Dec 12 2013

Keywords

Comments

a(45) > 1.5*10^13. - Bruce Garner, Jun 02 2021

Examples

			10 is a term because 1 plus the sum of the first 10 primes^17 is 7404514559506748686057600 which is divisible by 10.

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
    p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^17; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
Showing 1-10 of 12 results. Next

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