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A376118
Cryptarithmically unique palindromic primes.
1
11, 11141414111, 11999199911, 13111311131, 1110110110111, 1141411141411, 1611116111161, 3113113113113, 3222223222223, 3533355533353, 7444477744447, 7767777777677, 7887787877887, 7999979799997, 9494994994949, 9779999999779, 118818181818811, 131133131331131, 944499494994449, 10000010101000001
OFFSET
1,1
COMMENTS
The existence of terms >10^12 with 4 or more distinct digits has not been checked, so missing terms are possible but with a vanishing probability based on combinatorial arguments.
Each prime in this sequence is simultaneously a palindrome in base 10 and has a unique decimal digit pattern A358497(a(n)) in the sense that no other prime has the same pattern.
All terms except 11 have an odd number of digits (cf. A002385).
Number of terms < 100^k: 1, 1, 1, 1, 1, 4, 16, 19, 92, ... .
The smallest term with 3 distinct digits is 11155511521212511555111.
LINKS
EXAMPLE
11141414111 is a term since it's a palindromic prime and no other prime has the same pattern "AAABABABAAA" of repeating digits.
Counterexample: the palindromic prime 131 is not a term since another prime 151 has the same pattern "ABA" of repeating digits.
CROSSREFS
Intersection of A374238 and A002113.
Subsequence of A002385.
Supersequence of A004022 (prime repunits).
Cf. A358497.
Sequence in context: A275573 A247846 A257127 * A027569 A202282 A131680
KEYWORD
nonn,base
AUTHOR
Dmytro Inosov, Sep 11 2024
STATUS
approved