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 1-3 of 3 results.

A226692 The first member of a twin prime pair whose sum equals the sums of k consecutive smaller pairs of twin primes, k=3.

Original entry on oeis.org

59, 281, 347, 521, 569, 617, 1787, 2111, 4049, 4421, 5879, 6197, 8231, 9677, 10457, 11699, 12071, 12161, 12377, 14009, 16139, 17597, 17837, 21647, 22697, 33347, 36341, 39227, 41609, 43781, 44087, 46271, 48779, 51197, 53087, 56909, 58229, 58439, 64187
Offset: 1

Views

Author

Zak Seidov, Jun 15 2013

Keywords

Examples

			59 + 61 = (11 + 13) + (17 + 19) + (29 + 31) =  120,
281 + 283 = (71 + 73) + (101 + 103) + (107 + 109) = 564.

Links

Crossrefs

Cf. A225943 (k=2).

Programs

  • Mathematica
    s = Select[2*Range[40000], PrimeQ[# - 1] && PrimeQ[# + 1] &]; Intersection[s, Total /@ Partition[s, 3, 1]] - 1 (* T. D. Noe, Jun 17 2013 *)

A226652 Numbers n such that 6n -/+ 1 are twin prime pair and n = r + s where 6r -/+ 1 and 6s -/ 1 are consecutive smaller pairs of twin primes.

Original entry on oeis.org

3, 5, 12, 17, 110, 182, 217, 347, 352, 397, 432, 495, 707, 712, 775, 787, 822, 907, 920, 1115, 1127, 1265, 1370, 1500, 1722, 1810, 1860, 1953, 1995, 2167, 2742, 2943, 3087, 3372, 3713, 3840, 3985, 4030, 4153, 4580, 4762, 5093, 5750, 6018, 6540, 6920, 7263, 7355, 7367, 7378, 7637, 7957, 8727, 8932, 9002, 9340, 9368
Offset: 1

Views

Author

Zak Seidov, Jun 14 2013

Keywords

Comments

Terms in A002822 that are sum of some two subsequent terms.
Subsequence of terms of A225943 that are sum of some two subsequent terms, s2 = {17, 14745, 131010, 272125, 470573, 693635, 1393613, 1527925, 1953238, 3393075, 5219842, 5651810, 6662387, 10185065, 11332328, 11519365, 15051965}.
Is there similar subsequence s3 of s2, and so on?

Examples

			a(2) =  5 because A002822(4) = 5 = A002822(2)  + A002822(3) = 2 + 3.
a(3) =  12 because A002822(7) = 12 = A002822(4)  + A002822(5) = 5 + 7.

Links

Crossrefs

Cf. A002822 ( 6 n -/+ 1 are twin primes), A225943.

Formula

a(n) = (A225943(n)+1)/3.

A226719 a(n) = the first member of a twin prime pair whose sum equals the sums of n consecutive pairs of twin primes.

Original entry on oeis.org

3, 17, 59, 101, 107, 521, 239, 569, 881, 1427, 1091, 1289, 1301, 3167, 2027, 2309, 8837, 2969, 3389, 3821, 4787, 13679, 23909, 27407, 10889, 7877, 14627, 16631, 21011, 13997, 17027, 20441, 12107, 26711, 36467, 36779, 38567, 32909, 27479, 18521, 19751, 32057, 48479
Offset: 1

Views

Author

Zak Seidov, Jun 15 2013

Keywords

Comments

What is the origin of the lower bound of a(n), see graph?
Apparently a(n) > n^(5/2) but what about more strict bound?

Examples

			a(1) = 3 because 3 + 5 = 3 + 5 (trivial case)
a(2) = 17 = A225943(1)
a(3) = 59 = A226692(1)
a(4) = 101 because 101 + 103 = (11 + 13) + (17 + 19) + (29 + 31) + (41 + 43)
a(5) = 107 because 107 + 109 = (5 + 7) +  (11 + 13) + (17 + 19) + (29 + 31) + (41 + 43)

Links

Crossrefs

Cf. A226692 (three pairs), A225943 (two pairs).

Programs

  • Mathematica
    n = 1; t = {}; While[d = Intersection[s, Total /@ Partition[s, n, 1]]; Length[d] > 0, AppendTo[t, d[[1]] - 1]; n++]; t (* T. D. Noe, Jun 17 2013 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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