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 1-6 of 6 results.

A160358 Indices of primes in A133547, i.e., numbers n such that the sum of the squares of the first n odd primes is prime.

Original entry on oeis.org

3, 5, 9, 11, 23, 29, 63, 65, 71, 95, 141, 159, 161, 173, 179, 183, 209, 219, 255, 299, 323, 341, 365, 371, 389, 393, 453, 485, 521, 567, 579, 605, 623, 633, 635, 639, 677, 701, 711, 723, 725, 747, 785, 827, 867, 945, 981, 993, 999, 1001, 1013, 1035, 1037, 1041
Offset: 1

Views

Author

M. F. Hasler, May 18 2009

Keywords

Comments

All terms are necessarily odd. Thus one could also consider the sequence floor(a(n)/2) = (1,2,4,5,11,14,31,32,35,...). Other possible variations would be to list the index a(n)+1 of the largest prime in that sum, or, since this is always even, (a(n)+1)/2 = (2,3,5,6,12,15,32,33,36,...).

Crossrefs

Cf. A098561, A133547.

Programs

  • PARI
    s=0; for( i=2,1999, isprime(s+=prime(i)^2) & print1(i-1,","))

Formula

A160359(n) = A133547(a(n)) = A024450(a(n)+1) - 4.

A133548 a(n) = sum of cubes of first n odd primes.

Original entry on oeis.org

27, 152, 495, 1826, 4023, 8936, 15795, 27962, 52351, 82142, 132795, 201716, 281223, 385046, 533923, 739302, 966283, 1267046, 1624957, 2013974, 2507013, 3078800, 3783769, 4696442, 5726743, 6819470, 8044513, 9339542, 10782439, 12830822, 15078913, 17650266
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007, corrected Jun 08 2008

Keywords

Examples

			a(3)=495 because 3^3+5^3+7^3=495.

Links

Crossrefs

Cf. A007148, A007504, A024450, A098999, A133547, A133549, A133550, A133551.

Programs

  • Mathematica
    c = 3; a = {}; b = 0; Do[b = b + Prime[n]^c; AppendTo[a, b], {n, 2, 1000}]; a
Accumulate[Prime[Range[2,40]]^3] (* Harvey P. Dale, Oct 31 2024 *)
  • PARI
    a(n) = sum(i=2, n+1, prime(i)^3); \\ Michel Marcus, Nov 05 2013

Formula

a(n) = A098999(n+1) - 8.

Extensions

More terms from Michel Marcus, Nov 05 2013

A133550 Sum of fifth powers of n odd primes.

Original entry on oeis.org

243, 3368, 20175, 181226, 552519, 1972376, 4448475, 10884818, 31395967, 60025118, 129369075, 245225276, 392233719, 621578726, 1039774219, 1754698518, 2599294819, 3949419926, 5753649277, 7826720870, 10903777269, 14842817912
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Examples

			a(2)=3368 because 3^5+5^5 = 3368.

Crossrefs

Cf. A007148, A007504, A024450, A098999, A122102, A122103, A133547, A133548, A133550, A133551.

Programs

  • Mathematica
    c = 5; a = {}; b = 0; Do[b = b + Prime[n]^c; AppendTo[a, b], {n, 2, 1000}]; a

Formula

a(n) = A122103(n+1)-32.

A160359 Primes that are partial sums of squares of the odd primes.

Original entry on oeis.org

83, 373, 2393, 4723, 56383, 122701, 1789391, 1987849, 2706679, 7287991, 27833021, 41765519, 43570537, 55600477, 62283451, 67053359, 104720809, 122353547, 204330311, 347756707, 450504547, 540649093, 677774533, 715849843, 839886301
Offset: 1

Views

Author

M. F. Hasler, May 18 2009

Keywords

Comments

There is necessarily an odd number of terms in the sum a(n) = 3^2+5^2+...+p(k)^2, i.e. the index k=A160358(n)+1 of the last prime in this sum is even.

Links

Crossrefs

Cf. A098562, A133547.

Programs

  • Maple
    P:= select(isprime,[seq(i,i=3..10000,2)]):
S:= ListTools:-PartialSums(map(`^`,P,2)):
select(isprime,S); # Robert Israel, May 13 2024
  • Mathematica
    Select[Accumulate[Prime[Range[2,400]]^2],PrimeQ] (* Harvey P. Dale, Jul 17 2021 *)
  • PARI
    s=0; forprime( p=3,9999, isprime(s+=p^2) & print1(s","))

Formula

Equals A000040 intersect A133547.

A133549 Sum of the fourth powers of the first n odd primes.

Original entry on oeis.org

81, 706, 3107, 17748, 46309, 129830, 260151, 539992, 1247273, 2170794, 4044955, 6870716, 10289517, 15169198, 23059679, 35177040, 49022881, 69174002, 94585683, 122983924, 161934005, 209392326, 272134567, 360663848, 464724249, 577275130
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Examples

			a(2)=706 because 3^4 + 5^4 = 706.

Crossrefs

Cf. A007148, A007504, A024450, A098999, A122102, A133547, A133548, A133550, A133551.

Programs

  • Maple
    a:=proc (n) options operator, arrow: add(ithprime(j)^4, j=2..n+1) end proc: seq(a(n),n=1..26); # Emeric Deutsch, Oct 02 2007
  • Mathematica
    c = 4; a = {}; b = 0; Do[b = b + Prime[n]^c; AppendTo[a, b], {n, 2, 1000}]; a

Formula

a(n) = A122102(n+1) - 16. - Michel Marcus, Nov 05 2013

Extensions

Comment corrected by Michel Marcus, Nov 05 2013

A370633 Numbers k such that A372041(k) = 3.

Original entry on oeis.org

1, 2, 4, 5, 11, 14, 31, 32, 35, 47, 70, 79, 80, 86, 89, 91, 104, 109, 127, 149, 161, 170, 182, 185, 194, 196, 226, 242, 260, 283, 289, 302, 311, 316, 317, 319, 338, 350, 355, 361, 362, 373, 392, 413, 433, 472, 490, 496, 499, 500, 506, 517, 518, 520, 524, 530, 568, 574, 593
Offset: 1

Views

Author

Michel Lagneau, May 01 2024

Keywords

Comments

3 is the smallest positive value occurring in A372041 and occurs when the sum of the squares of the first 2*k+1 primes starting at 3 is a prime.

Examples

			k = 2 is a term since A372041(2) = 3, meaning that the sum of the 2*k+1 = 5 squares of primes starting at 3 is a prime: 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373.

Crossrefs

Cf. A133547, A160358, A372041.

Formula

a(n) = (A160358(n) - 1)/2.
Showing 1-6 of 6 results.

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