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A176465
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Palindromic primes p(k) = palprime(k) such that their sum of digits ("sod") equals sum of digits of their palprime index k.
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3
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13331, 1022201, 1311131, 3001003, 3002003, 100707001, 102272201, 103212301, 103323301, 103333301, 104111401, 105202501, 105313501, 105323501, 106060601, 111181111, 111191111, 112494211, 121080121, 140505041, 160020061, 160161061
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OFFSET
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1,1
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COMMENTS
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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)
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REFERENCES
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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
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LINKS
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EXAMPLE
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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)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 18 2010
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STATUS
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approved
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