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A076612
Palindromic numbers with nonprime middle digit.
1
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
1,2
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
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 *)
PROG
(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
CROSSREFS
Cf. A002113.
Sequence in context: A202262 A202266 A232541 * A182775 A046354 A046357
KEYWORD
easy,nonn,base
AUTHOR
Jani Melik, Oct 21 2002
STATUS
approved