A077293 Partition the concatenation 1234567...of natural numbers into successive strings nontrivially (a(n) is not equal to n) such that the n-th string is a multiple of n.

12, 34, 567, 8, 910, 111213141516, 17181920, 2122232425262728, 293031, 323334353637383940, 41424344454647, 48, 49505152535455565758596061626364, 6566, 676869707172737475, 767778798081828384, 85, 868788

Offset: 1

Author

Amarnath Murthy, Nov 03 2002

Keywords

• nonn
• base

Comments

a(1) = 12, a(n) = smallest concatenation of next successive natural numbers that is a multiple of n, or 0 if no such concatenation exists.

a(1) = 1 would have given a trivial sequence 1,2,3,4,5....

Every partial concatenation is a left substring of the concatenation of natural numbers.

Examples

			a(2) = 34 = 2*17; a(7) = 17181920 = 7*2454560.
		

Crossrefs

Cf. A077294, A088597, A088598.

Programs

PARI

lista(nn) = {my(k=0, m); for(n=1, nn, m=k++; while(m%n>0 || m==n, m=eval(Str(m, k++))); print1(m, ", ")); } \\ Jinyuan Wang, May 16 2020

Formula

a(n) = A077294(n)*n. - Jinyuan Wang, May 16 2020

Extensions

Corrected and extended by Ray Chandler, Oct 18 2003