The least number having n digits (chosen from 1, 3, 7, and 9) containing S000857(n) primes.
3, 37, 137, 1373, 31373, 313739, 1317971, 13179719, 113733797, 1797193373, 17971933739, 131797193373, 3137971933739, 31379719337397, 313797193373911, 3137971933739199
1
Note that in some cases, the (n+1)-th term merely has a digit appended to the n-th term.
After computing all 4^15 and 4^16 numbers, added 313797193373911 and 3137971933739199. - T. D. Noe, May 02 2016
T. D. Noe, Plot of 16 terms
Carlos B. Rivera, Prime Puzzle 823: String of digits 1379 full of primes
(Mma) digits = {1, 3, 7, 9}; t = Table[mx = 0; cnt = 0; Do[d = digits[[IntegerDigits[i, 4, numLen] + 1]]; t2 = Union[Flatten[Table[FromDigits[Take[d, {i, j}]], {i, numLen}, {j, i, numLen}]]]; len = Length[Union[Select[t2, PrimeQ]]]; If[len == mx, cnt++, If[len > mx, mx = len; cnt = 1; dBest = FromDigits[d]]], {i, 0, 4^numLen - 1}]; Print[{numLen, mx, dBest, cnt}]; {mx, dBest, cnt}, {numLen, 10}]; Transpose[t][[2]]
nonn,base,hard,more
T. D. Noe, Mar 29 2016