The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A090287 Smallest prime obtained by sandwiching n between a number with identical digits, or 0 if no such prime exists. Primes of the form k n k where all the digits of k are identical. 8
 101, 313, 727, 131, 11411, 151, 777767777, 373, 181, 191, 9109, 0, 7127, 331333, 991499, 1151, 3163, 1171, 1181, 9199, 1201, 112111, 0, 1231, 7247, 3253, 7777777777267777777777, 1111271111, 11128111, 1291, 1301, 3313, 1321, 0, 3343, 333533, 1361, 3373, 1381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) = 0 if n is a palindrome with even number of digits. Conjecture: No other term is zero. The conjecture is false.  a(231) = 0, a(420) = 0, a(n) = 0 if 11 divides n and n has an even number of digits. a(1414) has over 2000 digits. - Chai Wah Wu, Mar 31 2015 LINKS Chai Wah Wu, Table of n, a(n) for n = 0..365 Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015. MATHEMATICA (* f(n) defined by José de Jesús Camacho Medina in A010785. *) lst={}; f[m_]:=IntegerDigits[(m-9*Floor[(m-1)/9])*(10^Floor[(m+8)/9]-1)/9]; g[n_]:=FromDigits[Flatten[{f[m], IntegerDigits[n], f[m]}]]; Do[m=1; While[True, If[Mod[Length[IntegerDigits[n]], 2]==0&&IntegerDigits[n]==Reverse[IntegerDigits[n]], AppendTo[lst, 0]; Break[], If[PrimeQ[g[n]], AppendTo[lst, g[n]]; Break[]]]; m++], {n, 25}]; lst (* Ivan N. Ianakiev, Mar 23 2015 *) PROG (Python) from gmpy2 import is_prime, mpz, digits def A090287(n, limit=2000): ....sn = str(n) ....if n in (231, 420, 759) or not (len(sn) % 2 or n % 11): ........return 0 ....for i in range(1, limit+1): ........for j in range(1, 10, 2): ............si = digits(j, 10)*i ............p = mpz(si+sn+si) ............if is_prime(p): ................return int(p) ....else: ........return 'search limit reached.' # Chai Wah Wu, Mar 31 2015 CROSSREFS Cf. A010785, A338712. Sequence in context: A142578 A256048 A252942 * A134971 A082770 A161907 Adjacent sequences:  A090284 A090285 A090286 * A090288 A090289 A090290 KEYWORD base,nonn AUTHOR Amarnath Murthy, Nov 29 2003 EXTENSIONS a(0) from Chai Wah Wu, Mar 23 2015 a(26)-a(38) from Chai Wah Wu, Mar 24 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 18 15:09 EST 2022. Contains 350455 sequences. (Running on oeis4.)