A355700 - OEIS

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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.

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

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OFFSET

3,1

COMMENTS

All terms T(n,k) != -1, 2 < n <= 10 and 1 < k < n are emirps.

LINKS

Table of n, a(n) for n=3..38.

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

Adjacent sequences: A355697 A355698 A355699 * A355701 A355702 A355703

KEYWORD

sign,base,tabl

AUTHOR

Jean-Marc Rebert, Jul 14 2022

STATUS

approved