A351320 - OEIS

A351320

a(n) is the unique integer k such that k * A116436(n) = 1.A116436(n).1 where "." stands for concatenation.

111, 101, 87, 23, 21, 83, 21, 21, 27, 101, 87, 29, 23, 21, 33, 21, 83, 21, 39, 101, 87, 23, 21, 21, 21, 83, 101, 87, 59, 23, 21, 99, 57, 21, 27, 21, 101, 87, 29, 23, 21, 83, 69, 21, 71, 21, 101, 87, 33, 23, 21, 21, 83, 21, 101, 87, 23, 21, 27, 21, 39, 21, 83, 101, 87, 29, 23, 21, 21, 107, 21, 101

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OFFSET

1,1

COMMENTS

Except for a(1) = 111, which is unique, all terms appear infinitely many times and belong to this set of fifteen integers: {21, 23, 27, 29, 33, 39, 57, 59, 69, 71, 83, 87, 99, 101, 107}; see A329914.

The corresponding indices where these integers appear the first time are respectively: 5, 4, 9, 12, 15, 19, 33, 29, 43, 45, 6, 3, 32, 2, 70.

REFERENCES

David 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..72.

FORMULA

a(n) * A116436(n) = 1.A116436(n).1 where "." stands for concatenation.

EXAMPLE

A116436(1) = 1 and 111 * 1 = 1.1.1, hence a(1) = 111.

A116436(2) = 11 and 101 * 11 = 1.11.1, hence a(2) = 101.

A116436(32) = 112359550561797752809 and 99 * 112359550561797752809 = 1.112359550561797752809.1 hence a(32) = 99 (see Penguin reference).

PROG

(PARI) A116436(k) = {local(l, d, lb, ub); d=divisors(10^(k+1)+1); l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l}; \\ from A116436

a(n) = {my(v6=[], i=1); while (#v6 < n, v6 = concat(v6, A116436(i)); i++); my(x= v6[n]); my(k=1); while (eval(Str(1, x, 1)) % x, k++); eval(Str(1, x, 1))/x; } \\ Michel Marcus, Feb 10 2022

CROSSREFS

Cf. A116436, A329914, A329915.

M such that k*M=1M1 for: A095372 \ {1} (k=21), A331630 (k=23), A351237 (k=83), A351238 (k=87), A351239 (k=101).

Sequence in context: A282652 A282796 A282800 * A072807 A282976 A284083

Adjacent sequences: A351317 A351318 A351319 * A351321 A351322 A351323

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Feb 07 2022

STATUS

approved