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
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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;
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Mathematica
Select[Range[1000],PalindromeQ[#]&&OddQ[IntegerLength[#]]&&!PrimeQ[IntegerDigits[#][[(IntegerLength[#]+1)/2]]]&] (* Harvey P. Dale, Jun 15 2024 *)
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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
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