A309940 a(1) = 1, thereafter a(n) is the next prime after a(n-1), but written backwards in base n, then converted back to decimal.

1, 1, 2, 3, 1, 2, 3, 5, 7, 11, 23, 62, 31, 128, 173, 59, 173, 315, 263, 193, 177, 74, 233, 561, 347, 299, 281, 94, 293, 220, 193, 166, 71, 172, 1159, 428, 899, 1277, 1241, 391, 1157, 1245, 115, 1718, 533, 1621, 1397, 365, 1183, 1873, 2127, 2588, 2539, 317, 61

Offset

1,3

Comments

Conjecture: a(n) < n^2 for all n > 1.

From Robert Dougherty-Bliss, Sep 17 2019: (Start)

a(n) > n for n >= 10, as shown in the linked proof below.

The conjecture a(n) < n^2 holds for all 1 < n < N if each gap between consecutive squares < N contains a prime. In particular, the conjecture is true if Legendre's conjecture is true.

(End)

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Robert Dougherty-Bliss, Proof that a(n) > n for n >= 10

Example

The next prime after a(10) = 11 is 13:
- 13 in base 11 is "12",
- reading backwards we obtain "21" = 2*11 + 1 = 23,
- hence a(11) = 23.

Mathematica

nxt[{n_, p_}]:={n+1, FromDigits[Reverse[IntegerDigits[NextPrime[ p], n+1]], n+1]}; NestList[nxt, {1, 1}, 60][[All, 2]] (* Harvey P. Dale, Jul 29 2021 *)

Prog

(PARI) for (n=1, 55, print1 (v=if(n==1, 1, fromdigits(Vecrev(digits(nextprime(1+v), n)), n)) ", "))

Crossrefs

Cf. A326344.

The distinct numbers are listed in increasing order in A328076. See also A328257.

Sequence in context: A067280 A167157 A238837 * A081514 A109206 A292746

Adjacent sequences: A309937 A309938 A309939 * A309941 A309942 A309943

Keyword

nonn,base

Author

Rémy Sigrist, Sep 14 2019

Extensions

Name amended by Felix Fröhlich, Sep 16 2019

Status

approved