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

Author

Robert G. Wilson v, Jul 05 2024

Keywords

• base
• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

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]

Formula

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