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.

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A066869 Sum of the first n safe primes.

Original entry on oeis.org

5, 12, 23, 46, 93, 152, 235, 342, 509, 688, 915, 1178, 1525, 1884, 2267, 2734, 3213, 3716, 4279, 4866, 5585, 6424, 7287, 8174, 9157, 10176, 11363, 12646, 13953, 15272, 16639, 18078, 19565, 21088, 22707, 24530, 26437, 28464, 30503, 32566, 34665
Offset: 1

Views

Author

Joseph L. Pe, Jan 21 2002

Keywords

Comments

The subsequence of prime partial sums of safe primes begins: 5, 23, 509, 2267, 9157, 26437. The subsubsequence of safe prime partial sums of safe primes begins: 5, 23, and then what values? Note that A172037 Prime partial sums of Sophie Germain primes A005384 is related because 2p+1 is called a safe prime if p is a Sophie Germain prime. - Jonathan Vos Post, Jan 30 2010

Crossrefs

Cf. A005385.
Cf. A172037. - Jonathan Vos Post, Jan 30 2010

Programs

  • Mathematica
    Accumulate[Select[Prime[Range[350]],PrimeQ[(#-1)/2]&]] (* Harvey P. Dale, Jul 27 2011 *)

A325957 Sophie Germain primes equal to the sum of the first k Sophie Germain primes for some k.

Original entry on oeis.org

2, 5, 39233, 50969, 5402909, 6899969, 7722119, 10490933, 24296873, 46322183, 95837639, 117933353, 122693729, 132514703, 181862003, 303953873, 762321281, 929234279, 1044329843, 1150361501, 1335588539, 1353590321, 1662019811, 2048876033, 2176318433, 2250982931
Offset: 1

Views

Author

Metin Sariyar, Sep 10 2019

Keywords

Comments

The sum of first 268 terms of this sequence is also a Sophie Germain prime. 2 + 5 + 39233 + ... + 1187321288921 = 91753770231881.

Examples

			39233 is a term because sum of the first 56 Sophie Germain primes 2 + 3 + 5 + ... + 1811 = 39233 is prime and 39233*2+1 = 78467 is prime.

Links

Crossrefs

Cf. A000040, A005384, A005385, A013918, A066819, A172037.

Programs

  • Mathematica
    lst={}; s=0; Do[If[PrimeQ[n]&&PrimeQ[2*n+1], s=s+n; If[PrimeQ[s]&&PrimeQ[s*2+1], AppendTo[lst, s]]], {n, 1, 1000000}]; lst
  • PARI
    issg(p) = isprime(2*p+1);
lista(nn) = {my(s=0); forprime(p=2, nn, if (issg(p), s + = p; if (isprime(s) && issg(s), print1(s, ", "); ); ); ); } \\ Michel Marcus, Sep 11 2019

Formula

Equals A005384 Intersection A066819.
Showing 1-2 of 2 results.

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