A153353 - OEIS

%I #17 Sep 24 2017 11:22:40

%S 23,57,127131,937941,2087320879,6557965581,925039925051,

%T 14073611407383,89811798981191,94647139464723,1553629915536303,

%U 122504623122504633,200602291200602313,495401873495401911,133201458751133201458773

%N List of pairs of concatenated adjacent primes [p(n),p(n+1)] such that the concatenation is divisible by n.

%C The corresponding values of n are listed in A125085.

%C Subset of A045533. [_R. J. Mathar_, Jan 03 2009]

%e 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).

%e 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).

%p 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

%t 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 *)

%Y Cf. A007795, A045533, A095958.

%Y Cf. A000040.

%K nonn,base

%O 1,1

%A _Gil Broussard_, Dec 24 2008

%E 3 more terms from _R. J. Mathar_, Jan 03 2009

%E a(9)-a(14) from _Robert G. Wilson v_, Jan 23 2009

%E a(15) from _Donovan Johnson_, Aug 08 2010