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 1-4 of 4 results.

A070934 Smallest prime equal to the sum of 2n+1 consecutive primes.

Original entry on oeis.org

2, 23, 53, 197, 127, 233, 691, 379, 499, 857, 953, 1151, 1259, 1583, 2099, 2399, 2417, 2579, 2909, 3803, 3821, 4217, 4651, 5107, 5813, 6829, 6079, 6599, 14153, 10091, 8273, 10163, 9521, 12281, 13043, 11597, 12713, 13099, 16763, 15527, 16823, 22741
Offset: 0

Views

Author

Lekraj Beedassy, May 21 2002

Keywords

Examples

			Every term of the increasing sequence of primes 127, 401, 439, 479, 593,... is splittable into a sum of 9 consecutive odd primes and 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 is the least one corresponding to n = 4.

Links

Crossrefs

Cf. Bisection of A070281.
See A082244 for another version.
Cf. A089793, A215235.
Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, s},While[s = Sum[Prime[i], {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[f[n], {n, 0, 41}] (* Ray Chandler, Sep 27 2006 *)

Extensions

Corrected and extended by Ray G. Opao, Aug 26 2004
Entry revised by Ray Chandler, Sep 27 2006

A216004 Primes that are the sum of 2001 consecutive primes.

Original entry on oeis.org

16344247, 16588633, 16711217, 17416457, 17700139, 17806721, 17860039, 17895613, 18091313, 18144727, 18483739, 18573209, 18698791, 19040773, 19384609, 19529849, 19620719, 19748129, 19784543, 19802759, 20421971, 20476777, 20531593, 20806141, 21283169, 21356563
Offset: 1

Views

Author

Syed Iddi Hasan, Aug 30 2012

Keywords

Comments

Corresponding initial terms of 2001-tuples: 7, 61, 97, 313, 419, 449, 463, 479, 563, 577, 691, 733, 773, 911, 1039, 1093, 1123, 1187, 1201, 1213, 1459, 1483, 1493, 1607. The indices of these primes: 4, 18, 25, 65, 81, 87, 90, 92, 103, 106, 125, 130, 137, 156, 175, 183, 188, 195, 197, 198, 232, 235, 238, 253. - Zak Seidov, Feb 27 2013

Examples

			a(1) = sum(prime(k), k = 4..2004),  a(2) = sum(prime(k), k = 18..2018),... - _Zak Seidov_, Feb 27 2013

Links

Crossrefs

Cf. A070934, A082244, A215991.

Programs

  • Mathematica
    m = 2001; a = 2; b = Prime[m]; s = Sum[Prime[k], {k, m}]; Reap[Do[If[PrimeQ[s], Sow[s]]; b = NextPrime[b]; s = s - a + b; a = NextPrime[a], {m}]][[2, 1]] (* Zak Seidov, Feb 27 2013 *)
Select[Total/@Partition[Prime[Range[2500]],2001,1],PrimeQ] (* Harvey P. Dale, Mar 13 2018 *)

A379760 Smallest prime that is the sum of 2n+1 cubes of consecutive odd primes.

Original entry on oeis.org

66347, 15643, 81647, 279397, 1961623, 3701627, 5644601, 2505187, 8016551, 4695947, 9335519, 6819443, 12830327, 35259463, 35278489, 56759723, 39944393, 86442623, 186387137, 95860493, 118647143, 170943137, 118651139, 509399153, 241399309, 381448853, 877324879
Offset: 1

Views

Author

Michel Lagneau, Jan 02 2025

Keywords

Examples

			For n=2, the smallest sum of 2*n+1 = 5 cubed consecutive primes which is prime is a(2) = 7^3 + 11^3 + 13^3 + 17^3 + 19^3 = 15643.

Links

Crossrefs

Cf. A030078 (cube of primes), A082244 (analog for primes), A380319 (analog for square of primes).

Programs

  • Maple
    P3:= map(t -> t^3, select(isprime,[seq(i,i=3..10^5,2)])):
SP3:= ListTools:-PartialSums(P3):
f:= proc(n) local k;
  for k from 1 do if isprime(SP3[k+2*n+1]-SP3[k]) then return SP3[k+2*n+1]-SP3[k] fi od
end proc:
map(f, [$1..50]); # Robert Israel, Feb 02 2025
  • Mathematica
    a[n_] := Block[{k = 1, s}, While[s = Sum[Prime[i]^3, {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[a[n], {n, 1, 27}]
  • PARI
    a(n) = my(k=2, s = sum(i=0, 2*n, prime(k+i)^3)); while (!isprime(s), s -= prime(k)^3; k++; s += prime(k+2*n)^3;); s; \\ Michel Marcus, Jan 20 2025

A380319 Smallest prime that is the sum of 2n+1 squares of consecutive odd primes, or 0 if no such prime exists.

Original entry on oeis.org

83, 373, 1543, 2393, 4723, 10453, 0, 24953, 35323, 0, 56383, 98017, 0, 122701, 238879, 0, 263723, 318181, 0, 486617, 816547, 0, 874487, 817561, 0, 1130957, 1203343, 0, 3110867, 2451637, 1789391, 1987849, 2331379, 0, 2706679, 3124129, 0, 4260437, 4446319, 0
Offset: 1

Views

Author

Michel Marcus, Jan 20 2025

Keywords

Crossrefs

Cf. A001248 (primes squared), A082244 (analog for primes), A379760 (analog for cube of primes).

Formula

If n == 1 (mod 3), either a(n) = 0 or a(n) is the sum of the squares of the primes 3, 5, ..., prime(2*n+2), because p^2 == 1 (mod 3) for all primes p > 3 so the sum of 2*n+1 such primes is divisible by 3. - Pontus von Brömssen, Jan 20 2025

Extensions

Escape clause and more terms added by Pontus von Brömssen, Jan 20 2025
Showing 1-4 of 4 results.

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