A098563 -id:A098563 - cp's OEIS frontend

A098561 Numbers n such that the sum of the squares of the first n primes is prime.

2, 18, 26, 36, 68, 78, 144, 158, 164, 174, 192, 212, 216, 236, 264, 288, 294, 338, 344, 356, 384, 404, 416, 426, 500, 516, 518, 522, 534, 540, 548, 614, 678, 680, 782, 858, 866, 876, 878, 896, 900, 912, 950, 974, 996, 1064, 1080, 1082, 1100, 1122, 1158, 1160

Offset: 1

Rick L. Shepherd, Sep 14 2004

nonn

a(n) must clearly be even.

			2 is a term as the sum of the squares of the first two primes is 2^2 + 3^2 = 13, which is prime.

Zak Seidov, Table of n, a(n) for n = 1..1050

Cf. A098562 (corresponding primes), A024450 (sums of squares of primes), A098563 (sums of cubes of primes), A013916 (sums of primes).

Select[Range[1000], PrimeQ[Sum[Prime[i]^2, {i, #}]] &] (* Carl Najafi, Aug 22 2011 *)

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

Enoch Haga, May 15 2008

nonn

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).

			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.

Nathaniel Johnston, Table of n, a(n) for n = 1..1000
Carlos Rivera, Puzzle 443. Sum of cubes of consecutive primes, The Prime Puzzles and Problems Connection.

Cf. A066525, A098563, A140251.

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

Floor[CubeRoot[#]]^3&/@Select[Accumulate[Prime[Range[400]]^3],PrimeQ] (* Harvey P. Dale, May 22 2023 *)

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

Enoch Haga, May 15 2008

nonn

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

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

Nathaniel Johnston, Table of n, a(n) for n = 1..1000
Carlos Rivera, Puzzle 443. Sum of cubes of consecutive primes, The Prime Puzzles and Problems Connection.

Cf. A066525, A098563, A140250.

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

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

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A098561 Numbers n such that the sum of the squares of the first n primes is prime.

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

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A140251 Smallest cubes > terms in A066525.

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