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A338371 Integers for which there exists a self-repetition that is a term of A338166. 0
13, 17, 18, 19, 26, 31, 37, 39, 48, 49, 56, 62, 65, 71, 73, 79, 81, 84, 91, 93, 94, 97, 103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

Daniel Tsai, A recurring pattern in natural numbers of a certain property, arXiv:2010.03151 [math.NT], 2020.

Daniel Tsai, A recurring pattern in natural numbers of a certain property, Integers (2021) Vol. 21, Article #A32.

EXAMPLE

18 is a term since 1818 is a term of A338166.

48 is a term since 484848 is a term of A338166.

List of terms with their minimum number of repetitions : [13, 15], [17, 280], [18, 2], [19, 819], [26, 15], [31, 15], [37, 12], [39, 15], [48, 3], [49, 3243], [56, 3], [62, 15], [65, 3], [71, 280], [73, 12], [79, 624], [81, 2], [84, 3], [91, 819], [93, 15], [94, 3243], [97, 624], [103, 10234].

PROG

(PARI) f(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2])); \\ A338038

period(vp, n) = {my(p = 1, pten = 10^#Str(n)); for (i=1, #vp, if ((vp[i] != 2) && (vp[i] != 5), p = lcm(p, znorder(Mod(pten, vp[i]))); p = lcm(p, znorder(Mod(pten, vp[i]^2))); ); ); p; }

isok(n) = {my(r = fromdigits(Vecrev(digits(n)))); my(vp = setunion(factor(n)[, 1]~, factor(r)[, 1]~)); my(nbmax = period(vp, n)); if (nbmax == 1, nbmax = 2); my(krep=1); my(pten = 10^#Str(n)); for (k=2, nbmax, krep = pten*krep+1; my(q=1); for (i=1, #vp, my(va = valuation(krep, vp[i])); q *= vp[i]^va; ); if (f(n*q) == f(r*q), return(k); ); ); }

ispal(n) = my(d=Vecrev(digits(n))); n == fromdigits(d);

lista(nn) = {for (n=1, nn, if ((n % 10) && !ispal(n), if (isok(n), print1(n, ", ")); ); ); }

CROSSREFS

Cf. A338038, A338039, A338166.

Sequence in context: A084307 A066918 A164062 * A117326 A052055 A272119

Adjacent sequences: A338368 A338369 A338370 * A338372 A338373 A338374

KEYWORD

nonn,base,more

AUTHOR

Michel Marcus, Oct 23 2020

STATUS

approved

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Last modified January 29 21:02 EST 2023. Contains 359931 sequences. (Running on oeis4.)