A213537 - OEIS

%I #20 Jul 04 2018 05:50:48

%S 7,13,37,79,163,499,1279,2683,5503,11443,23977,48193,96457,194809,

%T 390739,781969,1563967,3128887

%N Record first differences of base sequence A213536 (a cousin prime recurrence sequence).

%C Much of the proved and observed behavior of prime generating sequences investigated by E. Rowland and also V. Shevelev is observed here as well.

%C Three conjectures on this sequence are formulated in A213536.

%H G. H. Hardy and J. E. Littlewood, <a href="https://dx.doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes</a>, Acta Mathematica, Vol. 44, pp. 1-70, 1923.

%H E. S. Rowland, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html">A natural prime-generating recurrence</a>, Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.

%H Pascal Sebah and Xavier Gourdon, <a href="http://numbers.computation.free.fr/Constants/Primes/twin.html">Introduction to twin primes and Brun’s constant</a>

%H V. Shevelev, <a href="http://arXiv.org/abs/0910.4676">A new generator of primes based on the Rowland idea</a>

%H V. Shevelev, <a href="http://arXiv.org/abs/0911.5478">Three theorems on twin primes</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dickson&#39;s_conjecture">Dickson's conjecture</a>

%e The first differences of A213536 are 7, 1, 1, 1, 1, 1, 13, 1, 5, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... The first two records are 7 and 13, which yield the first two terms of this sequence.

%Y Cf. A213536 (base sequence).

%K nonn,more

%O 1,1

%A _Joseph Benstock_, Jul 15 2012