Smallest prime of the form n xxxx…xxx for digit x, or 0 if there is none.
11, 2, 3, 41, 5, 61, 7, 83, 97, 101, 11, 127, 13, 149, 151, 163, 17, 181, 19, 2011, 211, 223, 23, 241, 251, 263, 271, 281, 29, 307, 31, 3299, 331, 347, 353, 367, 37, 383, 397, 401, 41, 421, 43, 443, 457, 461, 47, 487, 491, 503, 511111, 521, 53, 541, 557, 563, 571
1
Note the sequence is plotted using repeated logs because some terms are quite large. The first zero term is for 6930. This sequence was inspired by the paper of Wu. However, this work does not appear there. This sequence is not the same as A018800.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv 1503.0883 (Mar 31 2015)
(Mma) mx = 1000; Table[nDigits = IntegerDigits[n]; s = n; len = 0; i = 0; While[len < mx && ! PrimeQ[s], i++; If[i > 9, i = 1; len++]; s = FromDigits[Join[nDigits, Table[i, {len}]]]]; If[len < mx, s, 0], {n, 100}]
nonn,base,nice
T. D. Noe, Apr 09 2015