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 1-7 of 7 results.

A140250 a(n) is the largest cube <= A066525(n).

Original entry on oeis.org

343, 15625, 34965783, 106496424, 3023464536, 3659383421, 7222633237, 10403062487, 11179320256, 11993263569, 25881801912, 36495256013, 40672093519, 47516597848, 49917330568, 63616767488, 84200449887, 96323848704, 573234910443, 972947676429
Offset: 1

Views

Author

Enoch Haga, May 15 2008

Keywords

Comments

Suggested by Carlos Rivera's Prime Puzzles & Problems Connection, Puzzle 443 (which asks if a sum of consecutive cubes can be a cube or a prime cube).

Examples

			In A066525 the first term is 503, the sum of cubes of the first four consecutive primes, 2 3 5 7. The cube just less than 503 is 343, a(1) in this sequence.

Links

Crossrefs

Cf. A066525, A098563, A140251.

Programs

  • Maple
    with(numtheory): P:=proc(n) add(ithprime(k)^3,k=1..n): end:
A098563 := proc(n)local m: option remember: if(n=0)then return 0: fi: m:=procname(n-1)+2: while true do if(isprime(P(m)))then return m:fi: m:=m+2:od: end:
A140250 := proc(n)return floor(surd(P(A098563(n)),3))^3: end:
seq(A140250(n),n=1..20); # Nathaniel Johnston, Apr 21 2011
  • Mathematica
    Floor[CubeRoot[#]]^3&/@Select[Accumulate[Prime[Range[400]]^3],PrimeQ] (* Harvey P. Dale, May 22 2023 *)

Extensions

Edited by N. J. A. Sloane, Aug 25 2008
a(11)-a(20) from Nathaniel Johnston, Apr 21 2011

A140251 Smallest cubes > terms in A066525.

Original entry on oeis.org

512, 17576, 35287552, 107171875, 3029741623, 3666512088, 7233848504, 10417365504, 11194326053, 12008989000, 25908060079, 36528273432, 40707584000, 47555965367, 49958012987, 63664587657, 84258095104, 96386901625, 573441954112, 973242271000
Offset: 1

Views

Author

Enoch Haga, May 15 2008

Keywords

Examples

			The cube just greater than 503 is 512; a(1) in this sequence.

References

  • Suggested by Carlos Rivera's Prime Puzzles & Problems Connection, Puzzle 443 (which asks if the SCCP can be a cube or a prime cube).

Links

Crossrefs

Cf. A066525, A098563, A140250.

Formula

For each of the terms in A066525 (which are SCCP, sums of cubes of consecutive primes), find the cube just exceeding the term.

Extensions

a(11)-a(20) from Nathaniel Johnston, Apr 21 2011

A098562 Primes that are the sum of the squares of the first k primes for some k.

Original entry on oeis.org

13, 20477, 75997, 239087, 2210983, 3579761, 29194283, 40002073, 45448471, 55600481, 77290091, 108095623, 114986483, 155637463, 226226771, 302920139, 324657881, 519681709, 551321299, 618359839, 797005427, 944007487, 1039681147, 1124764853, 1923614047, 2135308631
Offset: 1

Views

Author

Rick L. Shepherd, Sep 14 2004

Keywords

Comments

These are the primes arising in A098561.

Examples

			From _K. D. Bajpai_, Dec 15 2014: (Start)
13 is in the sequence because the sum of the squares of the first 2 primes is 2^2 + 3^2 = 4 + 9 = 13, which is prime.
20477 is in the sequence because the sum of the squares of the first 18 primes is 2^2 + 3^2 + 5^2 + ... + 59^2 + 61^2 = 4 + 9 + 25 + ... + 3481 + 3721 = 20477, which is prime.
(End)

Links

Crossrefs

Cf. A098561 (corresponding n), A024450 (sum of squares of primes), A066525 (sums of cubes of primes), A013918 (sums of primes).
Cf. A000040, A006567. - Jonathan Vos Post, Aug 13 2009

Programs

  • Mathematica
    Select[Table[Sum[Prime[k]^2, {k, 1, n}], {n, 1000}], PrimeQ]  (* K. D. Bajpai, Dec 15 2014 *)
  • PARI
    s=0; forprime(p=2, 1e6, t=s+=p^2; if(isprime(t), print1(t,", "))) \\ K. D. Bajpai, Dec 15 2014

Extensions

a(24)-a(26) from K. D. Bajpai, Dec 15 2014
a(42) in b-file corrected by Andrew Howroyd, Feb 28 2018

A098563 Numbers n such that the sum of the cubes of the first n primes is prime.

Original entry on oeis.org

4, 8, 38, 48, 98, 102, 118, 128, 130, 132, 156, 168, 172, 178, 180, 190, 202, 208, 308, 346, 358, 364, 424, 482, 540, 600, 602, 614, 646, 676, 722, 748, 768, 776, 782, 792, 838, 902, 1016, 1028, 1036, 1058, 1062, 1082, 1086, 1100, 1102, 1132, 1144, 1176
Offset: 1

Views

Author

Rick L. Shepherd, Sep 14 2004

Keywords

Comments

n must clearly be even.

Examples

			4 is a term as the sum of the cubes of the first four primes is 2^3 + 3^3 + 5^3 + 7^3 = 503, which is prime.

Links

Crossrefs

Cf. A066525 (corresponding primes), A098561 (sums of squares of primes), A013916 (sums of primes), A098999 (sums of cubes of primes).

Programs

  • Maple
    with(numtheory): P:=proc(n) add(ithprime(k)^3, k=1..n): end:
A098563 := proc(n)local m: option remember: if(n=0)then return 0: fi: m:=procname(n-1)+2: while true do if(isprime(P(m)))then return m:fi: m:=m+2:od: end:
seq(A098563(n), n=1..50); # Nathaniel Johnston, Apr 21 2011
  • Mathematica
    Select[Range[1000], PrimeQ[Sum[Prime[i]^3, {i, #}]] &] (* Carl Najafi, Aug 22 2011 *)
  • PARI
    lista(nn) = {s = 0; ip = 0; forprime (p=1, nn, ip++; if (isprime(s+=p^3), print1(ip, ", ")););} \\ Michel Marcus, Aug 22 2015

A140596 Squares nearest to and < terms in A098562.

Original entry on oeis.org

9, 20449, 75625, 238144, 2208196, 3579664, 29192409, 39992976, 45441081, 55591936, 77281681, 108076816, 114982729, 155625625, 226201600, 302899216, 324648324, 519657616, 551310400, 618317956, 796989361, 943964176, 1039675536
Offset: 1

Views

Author

Enoch Haga, May 17 2008

Keywords

Examples

			The first term of A098562 is 13, the prime sum of 2^2=4 and 3^2=9. The square just preceding 13 is 9, the first term of this sequence.

Links

Crossrefs

Cf. A048760, A140597, A066525, A098561, A098562.

Formula

a(n) = A048760(A098562(n)). - Jason Yuen, Sep 30 2024

A140597 Squares nearest to and > terms in A098562.

Original entry on oeis.org

16, 20736, 76176, 239121, 2211169, 3583449, 29203216, 40005625, 45454564, 55606849, 77299264, 108097609, 115004176, 155650576, 226231681, 302934025, 324684361, 519703209, 551357361, 618367689, 797045824, 944025625, 1039740025
Offset: 1

Views

Author

Enoch Haga, May 17 2008

Keywords

Examples

			The first term of A098562 is 13, the prime sum of 2^2 + 3^2, where 4+9=13. The square just exceeding 13 is 16, the first term of this sequence.

Links

Crossrefs

Cf. A048761, A140596, A066525, A098561, A098562, A140250, A140251.

Formula

a(n) = A048761(A098562(n)). - Jason Yuen, Sep 30 2024

A368850 Primes that are equal to the sum of the first k proper prime powers for some k.

Original entry on oeis.org

37, 89, 3391, 6547, 10271, 20233, 88397, 2256827, 6160597, 11073263, 14337313, 15797057, 18938809, 24514339, 28298057, 29442893, 33119963, 40078453, 118950121, 128935063, 135825923, 154641481, 209301217, 244837321, 342462997, 471596659, 498175681
Offset: 1

Views

Author

Ilya Gutkovskiy, Jan 07 2024

Keywords

Examples

			37 is a term because 37 is a prime and 37 = 4 + 8 + 9 + 16 = 2^2 + 2^3 + 3^2 + 2^4.

Crossrefs

Cf. A000040, A013918, A025475, A066525, A098562, A246547.

Programs

  • Mathematica
    Select[Accumulate[Select[Range[5000000], PrimeOmega[#] > 1 && PrimePowerQ[#] &]], PrimeQ[#] &]
Showing 1-7 of 7 results.

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