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

Author

Bernard Schott, Nov 24 2019

Keywords

• nonn
• base
• fini
• full

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.

Examples

			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.
		

References

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

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}.