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A224220 a(n) = smallest number k with property that if the base-n expansion of k is reversed, the result is a nontrivial multiple of k. 1
32, 75, 8, 245, 12, 21, 16, 1089, 15, 1859, 21, 39, 28, 4335, 24, 6137, 24, 57, 40, 11109, 33, 115, 39, 45, 52, 22707, 35, 27869, 40, 93, 64, 55, 51, 47915, 57, 111, 76, 65559, 48, 75809, 56, 129, 88, 99405, 69, 329, 60, 119, 65, 143259, 72, 265, 63, 95, 112, 198417, 87, 219539 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

In other words, k divides (reversal of k in base n), and (k-reversed)/k > 1.

The numbers are written in base 10.

Theorem: The length of k (in base n) is 2 iff n>=5 and n+1 is composite, otherwise 4.

REFERENCES

N. J. A. Sloane, paper in preparation.

See A214927 for further references and links.

LINKS

Michel Marcus, Table of n, a(n) for n = 3..400

T. J. Kaczynski, Note on a Problem of Alan Sutcliffe, Math. Mag., 41 (1968), 84-86.

Lara Pudwell, Digit Reversal Without Apology, Mathematics Magazine, Vol. 80 (2007), pp. 129-132. Also arXiv:math/0511366 [math.HO], 2005.

Alan Sutcliffe, Integers That Are Multiplied When Their Digits Are Reversed, Mathematics Magazine, 39 (1966), 282-287.

FORMULA

If n=3 or n>3 and n+1 is prime, a(n) = (n^2-1)(n+1) (cf. A152619).

EXAMPLE

The numbers a(n) for n = 3, ..., 11 written in base n are 1012, 1023, 13, 1045, 15, 25, 17, 1089, 14.

For example, 1012 (base 3) = 32 (base 10), and 2101 (base 3) = 64 (base 10) = 2*32.

MATHEMATICA

Table[k = 2; While[Nand[IntegerQ@ #, # != 1] &[FromDigits[#, n]/k] &@ Reverse@ IntegerDigits[k, n], k++]; k, {n, 3, 60}] (* Michael De Vlieger, Feb 26 2017 *)

PROG

(PARI) isok(k, n) = {my(rk = fromdigits(Vecrev(digits(k, n)), n)); !(rk % k) && (rk > k); }

a(n) = {my(k = 1); while (!isok(k, n), k++); k; } \\ Michel Marcus, Feb 26 2017

CROSSREFS

Cf. A214927, A006093, A072668, A152619.

Sequence in context: A110230 A250756 A303583 * A007797 A222546 A240054

Adjacent sequences: A224217 A224218 A224219 * A224221 A224222 A224223

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Apr 01 2013

STATUS

approved

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Last modified January 26 20:46 EST 2023. Contains 359833 sequences. (Running on oeis4.)