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A088269
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Palindromic primes that yield a prime when sandwiched between two 1's. (Prefixing and suffixing a one on both sides yields another pal prime).
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5
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3, 5, 131, 383, 797, 11411, 16061, 16361, 19391, 33533, 36263, 73037, 75557, 79397, 1074701, 1126211, 1145411, 1175711, 1221221, 1243421, 1287821, 1303031, 1311131, 1328231, 1363631, 1489841, 1579751, 1600061, 1707071, 1748471
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| There are two 1-digit such n's, three 3-digit n's, nine 5-digit n's, 93 7-digit n's, 241 9-digit n's and no n with even number of digits. - Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..100
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EXAMPLE
| Start with 11;
insert a(2)=5 between digits of 11, 151 is prime;
insert a(3)=131 between digits of 11, 11311 is prime,
insert a(10)=33533 between digits of 11, 1335331 is prime, etc.
797 is a member as 17971 is also a prime.
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MATHEMATICA
| Do[If[PrimeQ[n] && Reverse[IntegerDigits[n]] == IntegerDigits[n] && PrimeQ[ToExpression["1" <> ToString[n*10+1]]], Print[n]], {n, 1, 2*10^6}] (Propper)
palsQ[n_]:=Module[{idn=IntegerDigits[n], idn1}, idn1=Join[{1}, idn, {1}]; idn==Reverse[idn]&&idn1==Reverse[idn1]&&PrimeQ[FromDigits[idn1]]]; Select[Prime[Range[150000]], palsQ] (* From Harvey P. Dale, Jan 04 2012 *)
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CROSSREFS
| Cf. A088270, A088271, A088272.
Sequence in context: A070743 A180541 A103993 * A164371 A108013 A087307
Adjacent sequences: A088266 A088267 A088268 * A088270 A088271 A088272
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KEYWORD
| base,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 28 2003
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jul 09 2005
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 29 2007
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