A374350 Least n-digit reversible prime whose difference from its reversal is minimal.

2, 11, 101, 1231, 10301, 105601, 1003001, 10012001, 100030001, 1007457001, 10000500001, 100124521001, 1000008000001, 10000523500001, 100000323000001, 1000034344300001, 10000000500000001, 100000188981000001, 1000000008000000001, 10000001189110000001, 100000000212000000001

Offset

1,1

Comments

Inspired by A084475 and A373349.

For n > 1, a(2n) has a difference of 9*10^n and a(2n-1) has a difference of 0.

Links

Table of n, a(n) for n=1..21.

Formula

a(2n-1) = A100027(n) = A028989(n).

Example

a(3) = 101 since its reversal is also 101;
a(4) = 1231 since its reversal is 1321 which is also prime and their difference is minimal at 90;
a(6) = 105601 since its reversal is 106501 which is also prime and their difference is minimal at 900;
a(8) = 10012001 since its reversal is 10021001 which is also prime and their difference is minimal at 9000; etc.

Mathematica

fe[n_] := Block[{k = 1, j, p, q}, While[ j = k(10^IntegerLength[k]) + IntegerReverse[k +1]; p = 10^(2 n -1) + j(10^(n - IntegerLength[j]/2)) + 1; q = IntegerReverse@ p; !PrimeQ@ p || !PrimeQ@ q, k++; If[ Mod[k, 10] == 9, k++]]; p]; fe[1] = 11;
fo[n_] := Block[{k = 0, j, p}, While[ j = k(10^(IntegerLength[k] -1)) + IntegerReverse@ Quotient[k, 10]; p = 10^(2n -2) + j(10^(n - (IntegerLength[j] + 1)/2)) +1; !PrimeQ@ p, k++]; p];
a[n_] := If[ OddQ@ n, fo[(n +1)/2], fe[n/2]]; Array[a, 21]

Crossrefs

Cf. A028989, A084475, A100027, A114018, A373349, A374377.

Sequence in context: A199302 A069663 A241100 * A337017 A121419 A099701

Adjacent sequences: A374347 A374348 A374349 * A374351 A374352 A374353

Keyword

base,nonn

Author

Robert G. Wilson v, Jul 05 2024

Status

approved