A076612 - OEIS

%I #23 Jun 15 2024 16:13:45

%S 1,4,6,8,9,101,111,141,161,181,191,202,212,242,262,282,292,303,313,

%T 343,363,383,393,404,414,444,464,484,494,505,515,545,565,585,595,606,

%U 616,646,666,686,696,707,717,747,767,787,797,808,818,848,868,888,898,909

%N Palindromic numbers with nonprime middle digit.

%C 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

%H Harvey P. Dale, <a href="/A076612/b076612.txt">Table of n, a(n) for n = 1..1000</a>

%p 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;

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

%o (Python)

%o from itertools import chain, count, islice

%o def A076612_gen(): # generator of terms

%o     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)))

%o A076612_list = list(islice(A076612_gen(),20)) # _Chai Wah Wu_, Jun 23 2022

%Y Cf. A002113.

%K easy,nonn,base

%O 1,2

%A _Jani Melik_, Oct 21 2002