A195302 -id:A195302 - cp's OEIS frontend

A215641 Smallest 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.

2, 211, 211151, 2111011129, 211101100910009, 211101100910007100049, 2111011009100071000031000453, 211101100910007100003100000310000721, 211101100910007100003100000310000019100000543, 2111011009100071000031000003100000191000000071000000531

Offset: 1

Jonathan Vos Post, Aug 18 2012

It is a plausible conjecture that a(n) always exists.

a(n) has A000217(n) = n*(n+1)/2 digits.

			a(4) = 2111011129, the smallest prime formed from a single-digit, a double-digit, a triple-digit, and a quadruple-digit prime, i.e., 2, 11, 101, 1129.

Cf. A000040, A000217, A003617.
Subsequence of A195302.
Cf. A338968 (similar, with largest prime).

Edited by N. J. A. Sloane, Aug 18 2012

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.

Original entry on oeis.org

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

Offset: 1

Bernard Schott, Dec 21 2020

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.

			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.

Cf. A000217, A003618, A215641.
Subsequence of A195302.
Cf. A339978 (with concatenated squares), A340115 (with concatenated cubes).

More terms from David A. Corneth, Dec 21 2020

cp's OEIS Frontend

A215641 Smallest 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.

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