A242541 Undulating primes: prime numbers whose digits follow the pattern A, B, A, B, A, B, A, B, ...

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

Offset: 1

Author

J. Lowell, May 17 2014

Keywords

• nonn
• base

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

Examples

			121 = 11*11 is not prime and thus is not a term of this sequence.
		

Links

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

Crossrefs

Cf. A004022, A032758, A033619.

Programs

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 *)

Python

from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
    yield from primerange(2, 100)
    yield from (t for t in (int((A+B)*d2+A) for d2 in count(1) for A in "1379" for B in "0123456789") if isprime(t))
print(list(islice(agen(), 51))) # Michael S. Branicky, Jun 09 2022