

A080340


First known infinite sequence containing no odd integer of the form 2^m+p (p prime).


3



7629217, 18814027, 29998837, 41183647, 52368457, 63553267, 74738077, 85922887, 97107697, 108292507, 119477317, 130662127, 141846937, 153031747, 164216557, 175401367, 186586177, 197770987, 208955797, 220140607, 231325417, 242510227
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OFFSET

0,1


COMMENTS

To a question of Romanoff: Are there infinitely many odd integers not of the form 2^m+p where p is prime? Erdõs answered Yes in 1950 by constructing the present sequence, an infinite arithmetic sequence, using a system of congruences.


LINKS

Table of n, a(n) for n=0..21.
P. Erdõs, On integers of form 2^n+p and some related problems, Summa Brasil Math.11 (1950), pp. 111
Tanya Khovanova, Recursive Sequences
T. Zamojski, Survey on covering congruences.
Index entries for linear recurrences with constant coefficients, signature (2, 1).


FORMULA

a(n) = n*11184810 + 7629217.


CROSSREFS

Sequence in context: A233605 A204803 A187962 * A192105 A233597 A258954
Adjacent sequences: A080337 A080338 A080339 * A080341 A080342 A080343


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Mar 19 2003


STATUS

approved



