

A191303


An infinite sequence of 4digit halfpalindromes.


0



52029, 316725, 1093345, 2811129, 6031029, 11445709, 19879545, 32288625, 49760749, 73515429, 104903889, 145409065, 196645605, 260359869, 338429929, 432865569, 545808285, 679531285, 836439489, 1019069529, 1230089749, 1472300205, 1748632665, 2062150609
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OFFSET

1,1


COMMENTS

For the definition of kdigit halfpalindromes, see A191279. Although there exist infinitely many polynomials taking only 3digit halfpalindrome values (see comment to A191279), only two polynomials are known with all values 4digit halfpalindromes. They are the polynomials P(n) which were discovered in SeqFan Discussion list from Mar 14 2011 and its double.
The sequence lists values of P(n). All these are odd. For a given k>=5, up to now it is unknown if there are polynomials taking only kdigit halfpalindrome values and it is unknown whether there exist infinitely many such numbers.
Conjecture. For every k>=2, there exists a polynomial of degree k taking only kdigit halfpalindrome values.


LINKS



FORMULA

a(n) = (2*n+2)(14*n+9)^3+(3*n+3)*(14*n+9)^2+(5*n+3)*(14*n+9)+(2*n+1) = (2*n+1)*(14*n+11)^3 +(5*n+3)*(14*n+11)^2 +(3*n+3)*(14*n+11) +(2*n+2), such that the bases b < c are b=14*n+9, c=14*n+11.
G.f. x*(52029+56580*x+30010*x^28636*x^3+1729*x^4) / (x1)^5.  R. J. Mathar, Jul 01 2012


MATHEMATICA

LinearRecurrence[{5, 10, 10, 5, 1}, {52029, 316725, 1093345, 2811129, 6031029}, 20] (* Harvey P. Dale, Sep 19 2018 *)


CROSSREFS



KEYWORD

nonn,easy,base


AUTHOR



STATUS

approved



