A230045 Palindromic primes with strictly increasing sum of digits.

2, 3, 5, 7, 181, 191, 373, 383, 727, 757, 787, 797, 17971, 19891, 19991, 76667, 77977, 78887, 79997, 1987891, 1988891, 1998991, 3799973, 3899983, 3998993, 7897987, 7996997, 9888889, 9889889, 9989899, 199999991, 768989867, 779969977, 779999977, 798989897

Offset

1,1

Comments

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

Links

Shyam Sunder Gupta, Table of n, a(n) for n = 1..63

Example

a(6) = 191, sum of digits is 11; a(7) = 373, sum of digits is 13 and 13 > 11.

Mathematica

a = {}; t = 0; Do[z = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z], s = Apply[Plus, IntegerDigits[z]]; If[s > t, t = s; AppendTo[a, z]]], {n, 10^5}]; a
nPal[n_]:=Module[{id=IntegerDigits[n], lid, flid2, revleft1, oklpl, lfpt1, new1, lfpt2, revleft2, new2}, lid=Length[id]; flid2=Floor[lid/2]; revleft1=Reverse[Take[id, flid2]]; oklpl=If[OddQ[lid], flid2+1, flid2]; lfpt1=Take[id, oklpl]; new1=FromDigits[Join[lfpt1, revleft1]]; lfpt2=IntegerDigits[FromDigits[lfpt1]+1]; revleft2=If[EvenQ[lid], Reverse[lfpt2], Reverse[Drop[lfpt2, -1]]]; new2=FromDigits[Join[lfpt2, revleft2]]; Which[Union[id]=={9}, n+2, new1>n, new1, True, new2]]; DeleteDuplicates[{#, Total[IntegerDigits[#]]}&/@Select[NestList[nPal[#]&, 2, 200000], PrimeQ], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Dec 07 2025 *)

Crossrefs

Cf. A002385, A061248.

Sequence in context: A064155 A230047 A230042 * A069803 A083184 A046478

Adjacent sequences: A230042 A230043 A230044 * A230046 A230047 A230048

Keyword

nonn,base

Author

Shyam Sunder Gupta, Oct 06 2013

Status

approved