cp's OEIS Frontend

A263299 Primes that are the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's.

%I A263299 #39 Jan 27 2019 16:03:34
%S A263299 131,11113111,1111211111,111113111111,11111143111111,
%T A263299 11111111111111111111111
%N A263299 Primes that are the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's.
%C A263299 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).
%C A263299 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.
%C A263299 Note that the middle term of a(2) is 13, not 3.
%C A263299 Next term is too large to include.
%C A263299 The next term has 513 digits. - _Harvey P. Dale_, Jan 27 2019
%H A263299 Chai Wah Wu, <a href="/A263299/b263299.txt">Table of n, a(n) for n = 1..8</a>
%e A263299 131 is in the list because 131 is a concatenation of 1, (1^2 + 1 + 1) = 3 and 1, and because 131 is prime.
%t A263299 Select[FromDigits/@Table[Join[PadRight[{},n,1],IntegerDigits[n^2+n+1],PadRight[{},n,1]],{n,20}],PrimeQ] (* _Harvey P. Dale_, Jan 27 2019 *)
%o A263299 (PARI) for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, n^2 + n + 1, (10^n - 1)/9))), print1(k", ")))
%o A263299 (Python)
%o A263299 from gmpy2 import is_prime
%o A263299 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
%Y A263299 Cf. A002061, A002275, A004022, A068817, A070220, A070746, A261364, A262399.
%K A263299 nonn,base
%O A263299 1,1
%A A263299 _Altug Alkan_, Oct 13 2015