A178654 Palindromic primes of the form (q//R(q))/11 where q is an emirp, R() denotes digit-reversal and // concatenation.

727, 10301, 14341, 16361, 18181, 30703, 1003001, 1145411, 1163611, 1201021, 1363631, 1452541, 3001003, 3425243, 3503053, 100030001, 102343201, 103212301, 105272501, 105343501, 107070701, 107121701, 112030211, 124525421, 125010521

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jun 01 2010

Keywords

• base
• nonn

Comments

Concatenation of the emirps q (A006567) and their digit-reversed variant yields the sequence q//R(q) = 1331, 1771, 3113, 3773, 7117, 7337, 7997,..

Further division of each term through 11 (in the spirit of A132286) yields the sequence 121, 161, 283, 343, 647, 667, 727, 889, 9791..

If such a term is a palindromic prime (A002385), it joins the sequence.

The sequence is generated by the emirps A006567(i) with i= 7, 10, 12, 14, 15, 17, 45, 59, 60, 63, 72, 77, 115, 139, 143, 280, 289,...

Examples

			79 = emirp(7), 97 = emirp(8), 7997 / 11 = 727 = palprime(15) is first term
113 = emirp(10), 311 = emirp(16), 113311 / 11 = 10301 = palprime(21) is 2nd term
14303 = emirp(414), 30341 = emirp(639), 1430330341 / 11 = 130030031 = palprime(1229), 26th term
		

References

• M. Gardner: Mathematischer Zirkus, Seite 259 ff., Ullstein Berlin-Frankfurt/M.-Wien, 1988
• W. Lietzmann: Sonderlinge im Reich der Zahlen, Duemmler, Bonn, 1948

Links

• Robert Israel, Table of n, a(n) for n = 1..2500
• H. Gabai and D. Coogan, On palindromes and palindromic primes, Math. Mag. 42, pp. 252-254, 1969.

Crossrefs

Cf. A002385, A006567, A155214