A213537 Record first differences of base sequence A213536 (a cousin prime recurrence sequence).

7, 13, 37, 79, 163, 499, 1279, 2683, 5503, 11443, 23977, 48193, 96457, 194809, 390739, 781969, 1563967, 3128887

Offset

1,1

Comments

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

Three conjectures on this sequence are formulated in A213536.

Links

Table of n, a(n) for n=1..18.

G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes, Acta Mathematica, Vol. 44, pp. 1-70, 1923.

E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.

Pascal Sebah and Xavier Gourdon, Introduction to twin primes and Brun’s constant

V. Shevelev, A new generator of primes based on the Rowland idea

V. Shevelev, Three theorems on twin primes

Wikipedia, Dickson's conjecture

Example

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.

Crossrefs

Cf. A213536 (base sequence).

Sequence in context: A336773 A118819 A118525 * A094069 A338812 A052378

Adjacent sequences: A213534 A213535 A213536 * A213538 A213539 A213540

Keyword

nonn,more

Author

Joseph Benstock, Jul 15 2012

Status

approved