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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 1 on both sides yields another palindromic 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
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OFFSET
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1,1
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COMMENTS
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There are two 1-digit terms, three 3-digit terms, nine 5-digit terms, 93 7-digit terms, 241 9-digit terms and no terms with an even number of digits. - Zak Seidov, Feb 23 2005
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..100
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EXAMPLE
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Take palindromic primes (A002385) and see whether inserting them between two digits '1' again yields a prime:
Insert a(1) = 3 between the digits of 11 to get 131, a prime.
Insert a(2) = 5 between the digits of 11 to get 151, a prime.
Inserting 11 between two '1's yields 1111 = 11 * 101, not a prime.
Insert a(3) = 131 between the digits of 11 to get 11311, a prime.
Insert a(10) = 33533 between the digits of 11 to get 1335331, a prime, etc.
797 is a term as 17971 is also a prime.
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MATHEMATICA
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Do[If[PrimeQ[n] && Reverse[IntegerDigits[n]] == IntegerDigits[n] && PrimeQ[ToExpression["1" <> ToString[n*10+1]]], Print[n]], {n, 1, 2*10^6}] (* Ryan Propper, Jul 09 2005 *)
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] (* Harvey P. Dale, Jan 04 2012 *)
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PROG
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(PARI) is_A088269(n)={isprime(n)&&(n=digits(n))==Vecrev(n)&&isprime(fromdigits(concat([1, n, 1])))} \\ M. F. Hasler, Nov 19 2018
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CROSSREFS
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Cf. A088270, A088271, A088272.
Cf. A002385.
Sequence in context: A240589 A180541 A103993 * A164371 A225672 A355803
Adjacent sequences: A088266 A088267 A088268 * A088270 A088271 A088272
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy, Sep 28 2003
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EXTENSIONS
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a(6)-a(30) from Ryan Propper, Jul 09 2005
Entry revised by N. J. A. Sloane, Apr 29 2007
Edited by M. F. Hasler, Nov 19 2018
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STATUS
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approved
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