

A338968


a(n) is the largest prime whose decimal expansion consists of the concatenation of a 1digit prime, a 2digit prime, a 3digit prime, ..., and an ndigit prime.


8



7, 797, 797977, 7979979941, 797997997399817, 797997997399991999371, 7979979973999919999839999901, 797997997399991999983999999199999131, 797997997399991999983999999199999989999997639, 7979979973999919999839999991999999899999999379999997871
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

It is a plausible conjecture that a(n) always exists and begins with 7.
The similar smallest primes are in A215641.
If a(n) exists, it has A000217(n) = n*(n+1)/2 digits.
a(1) = 7 = A003618(1) and a(2) = 797 is the concatenation of 7 = A003618(1) and 97 = A003618(2) that are respectively the largest 1digit prime and 2digit prime.
Conjecture: for n >= 3, a(n) is the concatenation of the largest kdigit primes with 1 <= k <= n1: A003618(1)/A003618(2)/.../A003618(n1) but the last concatenated prime with n digits is always < A003618(n). This conjecture has been checked by Daniel Suteu until a(360), a prime with 64980 digits.


LINKS

Table of n, a(n) for n=1..10.


EXAMPLE

a(3) = 797977 is the largest prime formed from the concatenation of a singledigit, a doubledigit, a tripledigit prime, i.e., 7, 97, 977.
a(4) = 7979979941 is the largest prime formed from the concatenation of a singledigit, a doubledigit, a tripledigit, and a quadrupledigit prime, i.e., 7, 97, 997, 9941.


CROSSREFS

Cf. A000217, A003618, A215641.
Subsequence of A195302.
Cf. A339978 (with concatenated squares), A340115 (with concatenated cubes).
Sequence in context: A014013 A001467 A342836 * A342834 A278438 A279120
Adjacent sequences: A338965 A338966 A338967 * A338969 A338970 A338971


KEYWORD

nonn,base


AUTHOR

Bernard Schott, Dec 21 2020


EXTENSIONS

More terms from David A. Corneth, Dec 21 2020


STATUS

approved



