A329915 a(n) is the least M such that A329914(n) * M = 1M1, where 1M1 denotes the concatenation of 1, M and 1.

91, 77, 5882353, 52631579, 4347826087, 3448275862069, 2127659574468085106383, 20408163265306122449, 1694915254237288135593220339, 16393442622950819672131147541, 137, 13, 112359550561797732809, 11, 10309278350515463917525773195876288659793814433

Offset

1,1

Comments

When M is a q-digit term, then M is a divisor of 10^(q+1) + 1.

For each term k in A329914, there exist a set of numbers M_k which, when 1 is placed at both ends of M_k, the number M_k is multiplied by k. This sequence gives the smallest integer M(k) = M of each set {M_k}.

See A329914 for further information about these numbers.

References

D. Wells, 112359550561797732809 entry, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1997, p. 196.

Links

Table of n, a(n) for n=1..15.

Example

A329914(1) = 21 and 21 * 91 = 1[91]1, and there is no integer < 91 that satisfies this relation, so a(1) = 91.
A329914(2) = 23 and 23 * 77 = 1[77]1, and there is no integer < 77 that satisfies this relation, so a(2) = 77.
A329914(5) = 33 and 33 * 4347826087 = 1[4347826087]1, and there is no integer < 4347826087 that satisfies this relation, so a(5) = 4347826087.

Crossrefs

Cf. A000533, A329914 (corresponding numbers k).

Some corresponding sets {M_k} : A095372 \ {1} = {M_21}, A331630 = {M_23}, A351237 = {M_83}, A351238 = {M_87}, A351239 = {M_101}.

Sequence in context: A180006 A259085 A033411 * A087411 A203363 A103847

Adjacent sequences: A329912 A329913 A329914 * A329916 A329917 A329918

Keyword

nonn,base,fini,full

Author

Bernard Schott, Nov 24 2019

Status

approved