

A242541


Undulating primes: prime numbers whose digits follow the pattern A, B, A, B, A, B, A, B...


4



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 18181, 32323, 35353, 72727, 74747, 78787, 94949, 95959, 1212121, 1616161, 323232323
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OFFSET

1,1


COMMENTS

All numbers in this sequence with three or more digits must have an odd number of digits. Any number with an even number of digits that follow this pattern is divisible by a number of the form 1010101...1010101 where the number of digits is one less than the number of digits in the original number.
Union of A004022 and A032758.  Arkadiusz Wesolowski, May 17 2014
Because A may equal B, 11 (and other prime repunits) are terms in this sequence (but not of A032758).  Harvey P. Dale, May 26 2015


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..135


EXAMPLE

121 = 11*11 is not prime and doesn't qualify for this sequence.


MAPLE

select(isprime, [$0..99, seq(seq(seq(a*(10^(d+1)10^(d+1 mod 2))/99 + b*(10^d  10^(d mod 2))/99, b=0..9), a=1..9, 2), d=3..9, 2)]); # Robert Israel, Jul 08 2016


MATHEMATICA

Select[Union[Flatten[Table[FromDigits[PadRight[{}, n, #]], {n, 9}]&/@ Tuples[ Range[0, 9], 2]]], PrimeQ] (* Harvey P. Dale, May 26 2015 *)


CROSSREFS

Cf. A004022, A032758, A033619.
Sequence in context: A049585 A049549 A030291 * A052085 A082646 A231588
Adjacent sequences: A242538 A242539 A242540 * A242542 A242543 A242544


KEYWORD

nonn,base


AUTHOR

J. Lowell, May 17 2014


STATUS

approved



