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

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

Author

Felix Fröhlich, Aug 25 2015

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Subsequence of A088882.

Cf. A001633, A002113, A210666.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Python

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

Formula

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