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A143867 a(n) = number of n-digit integers in which the first k digits are divisible by k-th prime. Leading zeros are not allowed. 2
4, 13, 26, 44, 39, 33, 24, 11, 4, 2 (list; graph; refs; listen; history; text; internal format)



For every 3-digit number, such a 4-digit number is guaranteed to exist - in a range of ten consecutive numbers, at least one of them must be divisible by 7. Since this is not true for 11 and greater, the number of eligible numbers goes down dramatically. 8757193191 and 6300846559 are the only 10-digit numbers to satisfy the requirements.


Table of n, a(n) for n=1..10.


There are four one-digit numbers divisible by 2 (the even, nonzero numbers), so a(1) = 4. For n = 2, the number must start with an even, nonzero digit and the second digit must make it divisible by 3, which gives 13 numbers: 21, 24, 27, 42, 45, 48, 60, 63, 66, 69, 81, 84 and 87. Appending a 0 or 5 to the end of any of these satisfies for a(3), so the count doubles to 26.


Cf. A079206 (the actual integers).

Sequence in context: A092484 A091823 A024834 * A024809 A212901 A049729

Adjacent sequences:  A143864 A143865 A143866 * A143868 A143869 A143870




Ellis M. Eisen (xerol(AT)xerol.org), Sep 04 2008



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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)