A110408 -id:A110408 - cp's OEIS frontend

A110409 Number of times repeated reverse concatenation of n followed by n gives a prime, where n == 1,3,7 or 9 (mod 10), or 0 if no such prime exists.

1, 0, 0, 0, 0, 10, 3, 7, 0, 3, 0, 10, 3, 0, 22, 0, 51, 7, 9, 10, 0, 412, 0, 16, 18, 0, 3, 0, 3, 3, 0, 9, 0, 3, 0, 3, 4, 0, 3, 0, 0

Offset: 0

Amarnath Murthy, Jul 30 2005

Except for the first term every nonzero term is >1.
The larger numbers are probable primes. - Joshua Zucker, May 10 2006
The sequence probably continues 0 0 10 0 0 0 0 0 0 4 0 0 0 130 6 0 0 0 4 0 0 0 0 0 6 6 0 0 4 0 4 0 0 0 0 0 10 10 34 0 0 0 0 but the 0's in that list that correspond to 103, 107, 113, 119, 133, 143, 157, 169, 187, 203, 209, are not proved (but if there is a term there, it is more than 500). - Joshua Zucker, May 10 2006
Not only must each nonzero term be >1 (to avoid divisibility by 11), it also cannot equal 2 (mod 3) to avoid divisibility by 3. - Joshua Zucker, May 10 2006

			The term corresponding to 19 is 7, as 7 concatenation of 91 followed by 19 is the least such prime. (9191919191919119 is a prime).

Cf. A110408.

More terms from Joshua Zucker, May 10 2006

Edited by T. D. Noe, Oct 30 2008

A260874 Smallest prime of the form p//r//p//r//p//r// ...., where p = prime(n), r = A004086(p) and // denotes concatenation.

Original entry on oeis.org

1331133113, 17711771177117711771177117711771177117711771177117711771177117711771177117, 19911991199119, 23322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223, 2992299229, 31133113311331

Offset: 6

Felix Fröhlich, Aug 02 2015

Felix Fröhlich, Table of n, a(n) for n = 6..100

Cf. A067087, A110408.

a(n) = p=prime(n); r=eval(concat(Vecrev(Str(p)))); s=eval(Str(p, r)); i=0; while(!ispseudoprime(s), if(i%2==0, s=eval(Str(s, p)); i++, s=eval(Str(s, r)); i++)); s

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A110409 Number of times repeated reverse concatenation of n followed by n gives a prime, where n == 1,3,7 or 9 (mod 10), or 0 if no such prime exists.

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A260874 Smallest prime of the form p//r//p//r//p//r// ...., where p = prime(n), r = A004086(p) and // denotes concatenation.

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