A153353 List of pairs of concatenated adjacent primes [p(n),p(n+1)] such that the concatenation is divisible by n.
23, 57, 127131, 937941, 2087320879, 6557965581, 925039925051, 14073611407383, 89811798981191, 94647139464723, 1553629915536303, 122504623122504633, 200602291200602313, 495401873495401911, 133201458751133201458773
Offset: 1
Examples
23 is a term because 2 and 3 are adjacent primes and 23 is divisible by 1 (the position of 2 in the sequence of primes). 127131 is a term because 127 and 131 are adjacent primes and 127131 is divisible by 31 (the position of 127 in the sequence of primes).
Programs
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Maple
A055642 := proc(n) max(1,ilog10(n)+1) ; end: cat2 := proc(a,b) a*10^A055642(b)+b ; end: A045533 := proc(n) cat2(ithprime(n),ithprime(n+1)) ; end: for n from 1 to 800000 do if A045533(n) mod n = 0 then printf("%d,",A045533(n)) ; fi; od: # R. J. Mathar, Jan 03 2009
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Mathematica
p = q = 2; c = 0; lst = {}; Do[c++; q = NextPrime@q; r = FromDigits@ Flatten[{IntegerDigits@ p, IntegerDigits@ q}]; If[Mod[r, c] == 0, AppendTo[lst, r]; Print[{c, r}]]; c++; q = NextPrime@ q; p = q, {n, 174254000}]; lst (* Robert G. Wilson v, Jan 23 2009 *)
Extensions
3 more terms from R. J. Mathar, Jan 03 2009
a(9)-a(14) from Robert G. Wilson v, Jan 23 2009
a(15) from Donovan Johnson, Aug 08 2010
Comments