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A323745 a(n) is the smallest prime that becomes composite if any single digit of its base-n 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 (list; graph; refs; listen; history; text; internal format)



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, ...


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


a(2)=3 because 3 is prime and its base-2 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 base-18 digits whose values are 13 and 14, respectively), and each of the 128 other base-18 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.


Cf. A186995.

Sequence in context: A069576 A249678 A300854 * A109899 A002297 A183270

Adjacent sequences:  A323742 A323743 A323744 * A323746 A323747 A323748




Jon E. Schoenfield, May 04 2019



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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)