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A220453 Numbers k such that right truncation of the decimal representation of k^k is never prime. 2

%I #40 Feb 12 2013 18:35:55

%S 1,2,6,10,16,20,76,92,100,108,109,115,125,129,136,201,227,317,400,405,

%T 427,451,477,518,575,594,606,649,659,836,858,901,960,995,1000,1022,

%U 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

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

%C 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 not-totally-clear-to-him 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.

%e The fact that 2^2 is a 1-digit 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.

%Y Cf. A220454.

%K nonn,base

%O 1,2

%A _James G. Merickel_, Dec 15 2012

%E a(62)-a(67) added by _James G. Merickel_, Feb 12 2013

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