

A263299


Primes that are the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's.


2




OFFSET

1,1


COMMENTS

Inspiration was a(6) that is concatenation of 10 1's, 10^2 + 10 + 1 and 10 1's. a(6) is R_23 and A004022(3).
k=1, 3, 4, 5, 6, 10 are initial values that generate primes in sequence. The consecutive central polygonal numbers associated with the four consecutive k are 13, 21, 31 and 43.
Note that the middle term of a(2) is 13, not 3.
Next term is too large to include.
The next term has 513 digits.  Harvey P. Dale, Jan 27 2019


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..8


EXAMPLE

131 is in the list because 131 is a concatenation of 1, (1^2 + 1 + 1) = 3 and 1, and because 131 is prime.


MATHEMATICA

Select[FromDigits/@Table[Join[PadRight[{}, n, 1], IntegerDigits[n^2+n+1], PadRight[{}, n, 1]], {n, 20}], PrimeQ] (* Harvey P. Dale, Jan 27 2019 *)


PROG

(PARI) for(n=1, 1e3, if(isprime(k=eval(Str((10^n  1)/9, n^2 + n + 1, (10^n  1)/9))), print1(k", ")))
(Python)
from gmpy2 import is_prime
A263299_list = [n for n in (int('1'*k+str(k*(k+1)+1)+'1'*k) for k in range(10**2)) if is_prime(n)] # Chai Wah Wu, Oct 19 2015


CROSSREFS

Cf. A002061, A002275, A004022, A068817, A070220, A070746, A261364, A262399.
Sequence in context: A033530 A222876 A267720 * A330202 A243832 A331909
Adjacent sequences: A263296 A263297 A263298 * A263300 A263301 A263302


KEYWORD

nonn,base


AUTHOR

Altug Alkan, Oct 13 2015


STATUS

approved



