A076612 Palindromic numbers with nonprime middle digit.

1, 4, 6, 8, 9, 101, 111, 141, 161, 181, 191, 202, 212, 242, 262, 282, 292, 303, 313, 343, 363, 383, 393, 404, 414, 444, 464, 484, 494, 505, 515, 545, 565, 585, 595, 606, 616, 646, 666, 686, 696, 707, 717, 747, 767, 787, 797, 808, 818, 848, 868, 888, 898, 909

Offset: 1

Author

Jani Melik, Oct 21 2002

Keywords

• easy
• nonn
• base

Comments

By definition, all terms have an odd number of digits. It is not surprising that the sequence of middle digits is 1, 4, 6, 8, 9, 0. - Harvey P. Dale, Jun 15 2024

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002113, A056525, A076609.

Programs

Maple

ts_num_midpal := proc(n) local ad,adr,midigit; ad := convert(n,base,10): adr := ListTools[Reverse](ad): if nops(ad) mod 2 = 0 then return 1; fi; midigit := op( (nops(ad)+1)/2,ad ): if (isprime( midigit )='false' and adr=ad) then return 0; else return 1; fi end: ts_n_pal := proc(n) if ts_num_midpal(n) = 0 then return (i) fi end: anpal := [seq(ts_n_pal(i), i=1..50000)]: anpal;

Mathematica

Select[Range[1000],PalindromeQ[#]&&OddQ[IntegerLength[#]]&&!PrimeQ[IntegerDigits[#][[(IntegerLength[#]+1)/2]]]&] (* Harvey P. Dale, Jun 15 2024 *)

Python

from itertools import chain, count, islice
def A076612_gen(): # generator of terms
    return chain((1,4,6,8,9),chain.from_iterable((int((s:=str(d))+e+s[::-1]) for d in range(10**l,10**(l+1)) for e in '014689') for l in count(0)))
A076612_list = list(islice(A076612_gen(),20)) # Chai Wah Wu, Jun 23 2022