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

1,2

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

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

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, A056525, A076609.

Sequence in context: A202266 A392354 A232541 * A182775 A046354 A046357

Adjacent sequences: A076609 A076610 A076611 * A076613 A076614 A076615

Keyword

easy,nonn,base

Author

Jani Melik, Oct 21 2002

Status

approved