A077186 Smallest multiple of prime(n) of the form 123...(k-1) k (k-1)...321 ( a concatenation of natural numbers from 1 to k and back to 1), or 0 if no such number exists.

0, 12321, 0, 12345654321, 121, 12345654321

Offset: 1

Author

Amarnath Murthy, Nov 01 2002

Keywords

• base
• nonn

Comments

a(7) has 435 digits (k=109) and is too large to include, a(8) has 399 digits (k=103), k(a(10))=1006, k(a(11))=17, k(a(12))=3 so a(12)=12321, k(a(13))=5 so a(13)=123454321, k(a(14))=103, k(a(17))=1019, k(a(18))=1002, k(a(19))=1001, k(a(20))=16. - R. J. Mathar, May 06 2006

Crossrefs

Cf. A077180, A077181, A077182, A077183, A077184, A077187, A077188, A173426.

Programs

PARI

palid(n)= { local(resul) ; resul=concat("",n) ; forstep(i=n-1,1,-1, resul=concat(i,resul) ; resul=concat(resul,i) ; ) ; return(eval(resul)) ; }
A077186(n)= { local(p) ; if(n==1 || n==3, return(0) ; ) ; p=prime(n) ; for(i=1,1500, if( palid(i)%p ==0, return(i) ; break ; ) ; ) ; return(-1) ; }
for(n=1,20, print("n=",n," k=",A077186(n)) ; ) ;  \\ R. J. Mathar, May 06 2006

Extensions

More terms from R. J. Mathar, May 06 2006