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A355700
Triangle T(n,k), n > 2, 1 < k < n, read by rows, where T(n,k) is in base n, the smallest prime consisting of digits d from a set of k nonzero consecutive digits, d times each, or -1 if no such number exists.
0
17, 41, 1787, 37, 1011749, -1, 8070191, 18919, 31783046759, -1, 107, 13588859, -1, 906611171779, 106661882252960131, 9883, 40487203, 173127971, 5664484284773, 696222287901816728317439, -1, 101, 97453813, -1, 28631342754671, 15215869393552811003, 629657070248572792452284791790843, -1, 32233, 123323, 334444555566656663, 122334444555553, 122334444555566566663, 1223334444555556666677767777, 22333444455555666666777777788888898999999989, -1
OFFSET
3,1
COMMENTS
All terms T(n,k) != -1, 2 < n <= 10 and 1 < k < n are emirps.
LINKS
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 33223
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 123323
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 122334444555553
EXAMPLE
T(3,2) = 17 = 122_3 is prime and has base-3 digits only from the set {1,2} with k=2 digits. In 122_3, the digit 1 occurs one time and the digit 2 two times. No lesser prime satisfies this.
T(10,3) = 123323 is prime and has only one 1, two 2's, three 3's, and the numbers 122333 = 71 * 1723, 123233 = 11 * 17 * 659 less than 123323 with the same digits are not prime.
Triangle begins:
17;
41, 1787;
37, 1011749, -1;
...
With the rows in base-n expansion:
n/k,2, 3, 4, 5, 6, ...
3, 122;
4, 221, 123323;
5, 122, 224333444, -1;
6, 444545555, 223331, 22333444554555, -1;
7, 212, 223334444, -1, 122333445544555, 122333444455555666666;
8, 23233, 232344443, 1224334443, 122333544554545, 223334444555556666777766777, -1;
9, 122, 223334444, -1, 122333444555455,
122333444455566666655, 22333444455555666666777778887888788, -1;
10, 32233, 123323, 334444555566656663, 122334444555553, 122334444555566566663, 1223334444555556666677767777, 22333444455555666666777777788888898999999989, -1;
11, 33232, 223343444, -1, ...
CROSSREFS
Sequence in context: A201028 A328022 A287308 * A090295 A191457 A191458
KEYWORD
sign,base,tabl
AUTHOR
Jean-Marc Rebert, Jul 14 2022
STATUS
approved