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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.

Index entries for primes involving decimal expansion of n

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

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