

A323745


a(n) is the smallest prime that becomes composite if any single digit of its basen expansion is changed to a different digit (but not to zero).


0



3, 2, 89, 67, 28151, 223, 6211, 2789, 294001, 701, 8399011, 2423, 691063, 243367, 527099, 10513, 2078920243, 10909, 169402249, 2114429, 156760543, 68543, 96733308587, 181141, 121660507, 6139219, 3141223681, 114493
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OFFSET

2,1


COMMENTS

This sequence has several terms in common with A186995; if the restriction that no digit can be changed to zero were removed, A186995 would result.
a(30) > 10^10.
The next few terms after a(30) are 356479, 860343287, 399946711, ...


LINKS

Table of n, a(n) for n=2..29.


EXAMPLE

a(2)=3 because 3 is prime and its base2 expansion is 11_2, which cannot have either of its digits changed to a nonzero digit, whereas the only smaller prime, i.e., 2 = 10_2, yields another prime if its 0 digit is changed to a 1.
a(3)=2 because 2 = 2_3 is prime and, in base 3, the only way to change its digit to another (nonzero) digit is to change it to 1_3 = 1, which is nonprime.
a(4)=89 because 89 = 1121_4 is prime, every number that can be obtained by changing one of its digits to another (nonzero) digit is nonprime (1122_4=90, 1123_4=91, 1111_4=85, 1131_4=93, 1221_4=105, 1321_4=121, 2121_4=153, 3121_4=217), and there is no prime smaller than 89 that has this property.
a(18)=2078920243 because 2078920243 = 3723de91_18 (where the letters d and e represent the base18 digits whose values are 13 and 14, respectively), and each of the 128 other base18 numbers that can be obtained by changing one of its eight digits to another (nonzero) digit is nonprime, and no smaller prime has this property.


CROSSREFS

Cf. A186995.
Sequence in context: A069576 A249678 A300854 * A109899 A002297 A183270
Adjacent sequences: A323742 A323743 A323744 * A323746 A323747 A323748


KEYWORD

nonn,base,more


AUTHOR

Jon E. Schoenfield, May 04 2019


STATUS

approved



