login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 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.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

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.

CROSSREFS

Cf. A220454.

Sequence in context: A137236 A124198 A032426 * A195957 A294013 A183575

Adjacent sequences:  A220450 A220451 A220452 * A220454 A220455 A220456

KEYWORD

nonn,base

AUTHOR

James G. Merickel, Dec 15 2012

EXTENSIONS

a(62)-a(67) added by James G. Merickel, Feb 12 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)