A175310 - OEIS

A175310

Let a(0) = 1. Either, a(n) = the smallest prime not yet occurring in the sequence that, when written in binary, it is a substring in the binary representation of a(n-1); or, if no such prime exists, a(n) = the smallest prime not yet occurring that when written in binary, a(n-1) is contained as a substring within it.

1, 2, 5, 11, 3, 7, 23, 47, 191, 31, 127, 383, 3067, 13, 29, 59, 239, 479, 223, 991, 61, 251, 503, 2039, 509, 1019, 4079, 16319, 65407, 1021, 4091, 24571, 4093, 16381, 98299, 6143, 63487, 3583, 15359, 129023

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Terms calculated by: (in alphabetical order) Ray Chandler, Charles R Greathouse IV, Hans Havermann, and D. S. McNeil.

LINKS

Table of n, a(n) for n=0..39.

H. Havermann, Binary Prime Cascade: A 3.4 MB file of 10000 formatted binary terms. The formatting consists of aligning the coincident parts of adjacent terms. In the event of ambiguity (as happens, for example, at indices 5, 9, and 10), the subsequent term is placed - for numbers smaller than their predecessor, as far to the left as possible, and for numbers greater than their predecessor, as far to the right as possible. Currently, the Safari web-browser will not display the file as intended. The gradual drift to the left continues beyond the 10000 terms shown. [From Hans Havermann, Apr 10 2010]

CROSSREFS

Cf. A175311.

Sequence in context: A215615 A018862 A332009 * A175311 A246208 A286091

Adjacent sequences: A175307 A175308 A175309 * A175311 A175312 A175313

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Mar 27 2010

STATUS

approved