A230042 Palindromic primes with strictly increasing product of digits.

2, 3, 5, 7, 181, 191, 353, 373, 383, 727, 757, 787, 797, 19891, 19991, 34843, 35753, 36563, 37573, 38783, 74747, 75557, 76667, 77977, 78787, 78887, 79997, 1987891, 1988891, 1998991, 3479743, 3487843, 3569653, 3586853, 3589853, 3689863, 3698963, 3799973

Offset: 1

Author

Shyam Sunder Gupta, Oct 06 2013

Keywords

• nonn
• base

Comments

a(1)=2; a(n+1) is the smallest palindromic prime with product of digits > product of digits of a(n).

Examples

			a(6) = 191, product of digits is 9; a(7) = 353, product of digits is 45 and 45 > 9.
		

Links

• Shyam Sunder Gupta and Chai Wah Wu, Table of n, a(n) for n = 1..200 (terms for n = 1..128 from Shyam Sunder Gupta)

Crossrefs

Cf. A002385, A230041, A007954, A053666.

Programs

Mathematica

a = {}; t = 0; Do[z = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z], s = Apply[Times, IntegerDigits[z]]; If[s > t, t = s; AppendTo[a, z]]], {n, 10^4}]; a
nxt[{p_,d_}]:=Module[{n=NextPrime[p]},While[!PalindromeQ[n]||Times@@ IntegerDigits[ n]<=d,n=NextPrime[n]];{n,Times@@IntegerDigits[n]}]; NestList[nxt,{2,2},40][[All,1]] (* Harvey P. Dale, Sep 30 2018 *)