A350153 Prime numbers created by concatenating all numbers 1 through k for some k > 1, then continuing to concatenate all numbers from k-1 towards 1. Primes are added to the sequence as they are found as k increases.

12343, 1234543, 12345678910987, 12345678910987654321, 12345678910111213141516171819202122212019181716151413, 12345678910111213141516171819202122232425262728293029

Offset

1,1

Comments

A173426(n) is the concatenation of all numbers from 1 up to k and then back down to 1. The prime terms of A173426 have been called "memorable primes" (see the Numberphile video). These "unmemorable primes" are a superset created by concatenating 1..k in ascending order followed by concatenating the numbers k-1..1 in descending order. Any primes found during either concatenation process are added to the sequence (e.g., k = 5, 1234543 is included. If 12345 were prime, it would be included as well).

Links

Patrick Quam, Table of n, a(n) for n = 1..29

Brady Haran and N. J. A. Sloane, The Most Wanted Prime Number, Numberphile video (2021).

Example

For k=10, the first prime obtained by concatenating the numbers 1..10 and then concatenating the first one or more numbers from 9..1 is 12345678910987.

Maple

select(isprime, [seq(seq(parse(cat($1..n, n-i$i=1..t)),
                t=0..n-1), n=1..30)])[];  # Alois P. Heinz, Dec 19 2021

Mathematica

lst={}; Table[s=Flatten[IntegerDigits/@Range@n]; k=n-1;
While[k!=-1, If[PrimeQ[p=FromDigits@s], AppendTo[lst, p]]; s=Join[s, IntegerDigits@k]; k--], {n, 100}]; lst (* Giorgos Kalogeropoulos, Dec 17 2021 *)

Prog

(Python)
from itertools import count, chain, islice, accumulate
from sympy import isprime
def A350153gen(): return filter(lambda p:isprime(p), (int(s) for n in count(1) for s in accumulate(str(d) for d in chain(range(1, n+1), range(n-1, 0, -1)))))
A350153_list = list(islice(A350153gen(), 20)) # Chai Wah Wu, Dec 20 2021

Crossrefs

Cf. A048847, A007908, A173426, A260343, A323532.

Sequence in context: A248717 A184472 A371833 * A251949 A178475 A104972

Adjacent sequences: A350150 A350151 A350152 * A350154 A350155 A350156

Keyword

nonn,base

Author

Patrick Quam, Dec 16 2021

Status

approved