A329931 Reversal of base-n digits of largest prime < n^3.

7, 23, 31, 89, 71, 97, 383, 647, 799, 967, 1151, 1507, 2351, 3149, 3583, 4045, 4535, 6497, 5599, 7937, 6775, 10579, 4607, 12499, 16223, 18953, 15679, 16819, 21599, 28829, 14335, 32669, 36991, 29399, 38879, 49283, 51983, 3041, 60799, 63877, 56447, 55469, 38719

Offset

2,1

Comments

Terms are listed in decimal.

Conjecture: a(n) < prevprime(n^3) for n >= 4. In other words, the most-significant base-n digit is larger than the least-significant base-n digit. This conjecture seems to hold for the analogous sequence with n^2, but fails for powers higher than 3.

Links

Table of n, a(n) for n=2..44.

Example

For n = 3, prevprime(3^3) = 23 = 212_3, and reversal gives a(3) = 212_3 = 23. For n = 5, prevprime(5^3) = 113 = 423_5, and reversal gives a(5) = 324_5 = 89.

Mathematica

a[n_] := FromDigits[ Reverse@ IntegerDigits[ NextPrime[n^3, -1], n], n]; Array[a, 43, 2] (* Giovanni Resta, Nov 24 2019 *)

Prog

(PARI) a(n) = fromdigits(Vecrev(digits(precprime(n^3-1), n)), n); \\ Michel Marcus, Nov 25 2019

Crossrefs

Base-n reversal of A077037(n).

Sequence in context: A295196 A287309 A275777 * A157811 A341284 A227421

Adjacent sequences: A329928 A329929 A329930 * A329932 A329933 A329934

Keyword

nonn,easy,base

Author

Robert Dougherty-Bliss, Nov 24 2019

Status

approved