A176465 Palindromic primes p(k) = palprime(k) such that their sum of digits ("sod") equals sum of digits of their palprime index k.

13331, 1022201, 1311131, 3001003, 3002003, 100707001, 102272201, 103212301, 103323301, 103333301, 104111401, 105202501, 105313501, 105323501, 106060601, 111181111, 111191111, 112494211, 121080121, 140505041, 160020061, 160161061

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 18 2010

Keywords

• base
• nonn

Comments

p(k) = palprime(k) (see A002385) with sod(p(k)) = sod(k)

List of (p(k),k):

(13331,29) (1022201,116) (1311131,173) (3001003,304) (3002003,305)

(100707001,790) (102272201,818) (103212301,832) (103323301,835) (103333301,836)

(104111401,850) (105202501,862) (105313501,865) (105323501,866) (106060601,875)

(111181111,961) (111191111,962) (112494211,979) (121080121,1096) (140505041,1379)

(160020061,1672) (160161061,1678) (160171061,1679) (181111181,1958) (300151003,2209)

(310131013,2344) (313222313,2387) (320444023,2488) (321242123,2495) (341040143,2765)

(341222143,2767) (342020243,2774) (342202243,2776) (342212243,2777) (342313243,2779)

(343050343,2788) (700090007,3488) (730111037,3884) (910212019,4858)

Examples

			p(1) = 13331 = palprime(29), sod(p(1)) = 1+3+3+3+1 = 11 = sod(29), first term
p(8) = 103212301 = palprime(832), sod(p(8)) = 1+0+3+2+1+2+3+1 = 13 = 8+3+2 = sod(832), 8th term
p(?) = 156300010003651 = palprime(99643), sod(p(?)) = 31 = sod(99733)
Note successive p(i) and p(i+1) which are also consecutive palindromic primes (i = 4, 9, 13, 16, 22, 33)
		

References

• A. H. Beiler: Recreations in the Theory of Numbers: The Queen of Mathematical Entertains. Dover Publications, New York, 1964
• M. Gardner: Mathematischer Zirkus , Ullstein Berlin-Frankfurt/Main-Wien, 1988
• K. G. Kroeber: Ein Esel lese nie. Mathematik der Palindrome, Rowohlt Tb., Hamburg, 2003

Crossrefs

A000213, A002385, A033548, A155214, A176111