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

1,1

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)

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

Links

Table of n, a(n) for n=1..22.

Example

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)

Crossrefs

A000213, A002385, A033548, A155214, A176111

Sequence in context: A283155 A254851 A162423 * A185503 A333014 A205196

Adjacent sequences: A176462 A176463 A176464 * A176466 A176467 A176468

Keyword

base,nonn

Author

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

Status

approved