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| A254928
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Smallest (nontrivial) prime that, for each k from 2 to n, remains prime when each digit is replaced by the digit's k-th power.
(history;
published version)
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#32 by Jon E. Schoenfield at Sat Dec 10 19:37:07 EST 2016
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#31 by Jon E. Schoenfield at Sat Dec 10 19:37:04 EST 2016
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| NAME
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Smallest (non-trivialnontrivial) prime that, for each k from 2 to n, remains prime when each digit is replaced by the digit's k-th power.
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| COMMENTS
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Examples of trivial primes are 11, 101, etc, i.e, ., all primes in the sequence A020449: these generate themselves for all powers. These primes are excluded, otherwise all terms would be 11 since sequence wants smallest primes.
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| STATUS
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approved
editing
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#30 by Kellen Myers at Thu Jun 11 16:10:56 EDT 2015
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#29 by Michel Marcus at Sun May 31 01:15:34 EDT 2015
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#28 by Michel Marcus at Sun May 31 01:14:42 EDT 2015
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| COMMENTS
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Examples of trivial primes are 11, 101, etc, i.e, all primes in the sequence A020449: these generate themselves for all powers. These primes are excluded, otherwise all terms would be of11 thesince sequence wouldwants besmallest 11primes.
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| EXAMPLE
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a(45) = 137; (1^k)&(3^k)&(7^k), where "&" represents concatenation of numbers:
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proposed
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Discussion
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| Sun May 31
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| Michel Marcus: slight edit to comment
example : 137 is a(5) because of offset 2
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#27 by Giovanni Resta at Tue May 19 06:05:20 EDT 2015
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#26 by Giovanni Resta at Tue May 19 06:05:12 EDT 2015
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| DATA
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13, 13, 13, 137, 157163, 153391501, 153391501, 1126903901803
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| EXTENSIONS
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a(9) from Giovanni Resta, May 19 2015
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| STATUS
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#25 by Michel Marcus at Mon May 18 00:21:18 EDT 2015
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#24 by Michel Marcus at Mon May 18 00:18:36 EDT 2015
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| COMMENTS
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Examples of trivial primes are 11, 101, etc, i.e, all primes in the sequence A020449: these generate themselves for all powers. These primes are excluded, otherwise all terms of the sequence would be 11.
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proposed
editing
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Discussion
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| Mon May 18
| 00:21
| Michel Marcus: Tried to develop the comment, but I think it still needs some improvement.
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#23 by Michel Marcus at Mon May 18 00:11:22 EDT 2015
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