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A082935 Smallest palindrome beginning with n and a digit sum of n at some stage. 0
1, 2, 3, 4, 5, 6, 7, 8, 9, 10801, 11711, 12621, 13531, 14441, 15351, 16261, 17171, 1881, 1949999999999999999999491, 208802, 2139312, 227722, 2329232, 246642, 2519152, 265562, 27972, 28882, 29792, 3088803, 3179713, 3278723, 3369633, 3468643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In most cases (perhaps in all other) except for n = 19 the digit sum in the first round itself is n. In case of 19 the first round of digit sum is 199 and the second round digit sum is 19.

Checked the conjecture above to n=100. - Robert G. Wilson v

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

a(19)=1949999999999999999999491. The smallest such number is 194 followed by 19 nines followed by 491. The first digit sum would be 199 and the next sum is 19.

MATHEMATICA

(*This code works for all numbers up to 100 except 19*) NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1;

idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]]]]]]; f[n_] := Block[{k = 1, dn = IntegerDigits[n]}, sdn = 2*Plus @@ dn; If[sdn == 2n, n, If[sdn == n, FromDigits[ Join[dn, Reverse[dn]]], If[sdn > n, 0, k = 10^Floor[(n - sdn)/9] - 1;; While[Plus @@ IntegerDigits[k] + sdn != n, k = NextPalindrome[k]]; FromDigits[ Join[dn, IntegerDigits[k], Reverse[dn]]]]]]]; Table[ f[n], {n, 1, 35}]

CROSSREFS

Cf. A082217.

Sequence in context: A135385 A087051 A082217 * A077739 A078213 A248794

Adjacent sequences:  A082932 A082933 A082934 * A082936 A082937 A082938

KEYWORD

base,nonn

AUTHOR

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 16 2003

EXTENSIONS

Edited, corrected and extended by Robert G. Wilson v, Jun 27 2003

STATUS

approved

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Last modified March 26 00:29 EDT 2019. Contains 321479 sequences. (Running on oeis4.)