A088882 -id:A088882 - cp's OEIS frontend

A325323 Palindromes in base 10 that are not Brazilian.

1, 2, 3, 4, 5, 6, 9, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 787, 797, 919, 929, 10201, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181, 18481, 19391, 19891, 19991

Offset: 1

Bernard Schott, Apr 20 2019

The terms >= 11 of this sequence are either prime palindromes which are not Brazilian, or square of primes (except 121).

Amiram Eldar, Table of n, a(n) for n = 1..1000

Intersection of A002113 and A220570.
Complement of A325322 with respect to A002113.
Cf. A088882 (Palindromes not repdigits).

brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length @ Union[IntegerDigits[n, b]] > 1, b++]; b < n - 1]; Select[Range[20000], PalindromeQ[#] && !brazQ[#] &] (* Amiram Eldar, Apr 14 2021 *)

isb(n) = for(b=2, n-2, my(d=digits(n, b)); if(vecmin(d)==vecmax(d), return(1))); \\ A125134
isp(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113
isok(n) = !isb(n) && isp(n); \\ Michel Marcus, Apr 22 2019

A261453 Near-repdigit palindromes with an odd number of digits and all digits except the middle digit equal.

Original entry on oeis.org

101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 565, 575, 585, 595, 606, 616, 626, 636, 646, 656, 676

Offset: 1

Felix Fröhlich, Aug 25 2015

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..171 from R. J. Mathar)

Subsequence of A088882.

Cf. A001633, A002113, A210666.

isA261453 := proc(n)
    local ndgs,dgs,d ;
    if isA002113(n) then
        ndgs := A055642(n) ;
        if type(ndgs,'odd') and A043537(n) = 2 then
            dgs := convert(n,base,10) ;
            for d from 2 to nops(dgs)/2 do
                if op(d,dgs) <> op(d-1,dgs) then
                    return false;
                end if;
            end do:
            true ;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
n := 1:
for i from 100 to 2000000 do
    if isA261453(i) then
        printf("%d %d\n",n,i) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Sep 30 2015

id[n_]:=IntegerDigits[n];len[n_]:=Length[id[n]];
del[n_]:=Delete[id[n],Ceiling[len[id[n]]/2]];
u[n_]:=Union[del[id[n]]];
Select[Range[10^5],StringMatchQ[ToString[#],a__~~b_~~a__]&&Length[u[#]]==1&&u[#]!= Union[id[#]]&] (* Ivan N. Ianakiev, Sep 06 2015 *)
Select[Flatten[Table[FromDigits[Join[PadRight[{},n,rd],{k},PadRight[{},n,rd]]],{n,3},{rd,9},{k,0,9}]],Count[DigitCount[#],0]==8&] (* Harvey P. Dale, Nov 30 2024 *)

is_a002113(n) = my(d=digits(n)); d==Vecrev(d)
is_a210666(n) = my(d=digits(n)); #d>2 && (#setintersect(vecsort(d), vector(#d, x, vecmax(d)))==#d-1 || #setintersect(vecsort(d), vector(#d, x, vecmin(d)))==#d-1)
is_a001633(n) = #Str(n)%2 \\ after Charles R Greathouse IV in A001633
is(n) = is_a002113(n) && is_a210666(n) && is_a001633(n) \\ Felix Fröhlich, May 25 2022

from itertools import count, islice
def agen(): # generator of terms
    for d in count(1):
        for out in "123456789":
            for mid in "0123456789":
                if mid != out:
                    yield int(out*d + mid + out*d)
print(list(islice(agen(), 52))) # Michael S. Branicky, May 17 2022

a(n) = A002113(A210666(A001633(n))).

cp's OEIS Frontend

A325323 Palindromes in base 10 that are not Brazilian.

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