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 A263299 Primes that are the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's. 2
 131, 11113111, 1111211111, 111113111111, 11111143111111, 11111111111111111111111 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 5 23:38 EST 2021. Contains 349558 sequences. (Running on oeis4.)