A338968 a(n) is the largest prime whose decimal expansion consists of the concatenation of a 1-digit prime, a 2-digit prime, a 3-digit prime, ..., and an n-digit prime.

7, 797, 797977, 7979979941, 797997997399817, 797997997399991999371, 7979979973999919999839999901, 797997997399991999983999999199999131, 797997997399991999983999999199999989999997639, 7979979973999919999839999991999999899999999379999997871

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 1-digit prime and 2-digit prime.

Conjecture: for n >= 3, a(n) is the concatenation of the largest k-digit primes with 1 <= k <= n-1: A003618(1)/A003618(2)/.../A003618(n-1) 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 single-digit, a double-digit, a triple-digit prime, i.e., 7, 97, 977.
a(4) = 7979979941 is the largest prime formed from the concatenation of a single-digit, a double-digit, a triple-digit, and a quadruple-digit 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