

A220453


Numbers k such that right truncation of the decimal representation of k^k is never prime.


2



1, 2, 6, 10, 16, 20, 76, 92, 100, 108, 109, 115, 125, 129, 136, 201, 227, 317, 400, 405, 427, 451, 477, 518, 575, 594, 606, 649, 659, 836, 858, 901, 960, 995, 1000, 1022, 1091, 1150, 1152, 1233, 1498, 1516, 1641, 1655, 1761, 1818, 1923, 1937, 1944, 1970, 2135, 2246, 2549, 2574, 2614, 2700, 2807, 2834, 2865, 3195, 3232, 3329, 3367, 3474, 3514, 3749, 3751
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OFFSET

1,2


COMMENTS

A220454 gives k such that the smallest prime in a left segment of k^k for those numbers excluded from this sequence sets a record. The tentative conclusion of the author at time of submission is that this sequence is after some point identical with the powers of 10 (would be finite, eventually, if they were excluded), with a nottotallycleartohim heuristic argument of modest complexity involving the Prime Number Theorem and comparisons of terms and factors in probabilities involving the exponential and logarithm functions to get an overall comparison with geometric series. So, though this sequence is currently more filled out than its companion, that sequence should eventually catch up and pass this one based on the arguments presented in its COMMENTS section.


LINKS



EXAMPLE

The fact that 2^2 is a 1digit composite automatically places 2 in the list, while the fact that the leading digit of both 3^3 and 4^4 is the prime 2 automatically excludes 3 and 4. 5^5 leads with the digit 3 and so 5 is similarly excluded, while lopping off any number of the rightmost digits of 6^6 leaves a composite, placing 6 in the sequence.


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



