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A076612
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Palindromic numbers with nonprime middle digit.
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MAPLE
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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
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Select[Range[1000], PalindromeQ[#]&&OddQ[IntegerLength[#]]&&!PrimeQ[IntegerDigits[#][[(IntegerLength[#]+1)/2]]]&] (* Harvey P. Dale, Jun 15 2024 *)
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PROG
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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)))
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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