A329542 a(n) is the first occurrence of a composite number whose factorization without exponents contains exactly n circular loops (i.e., loops in digits 0, 6, 8, 9) on each side of the equals sign.

76, 166, 801, 8067, 38804, 88181, 586668, 3680818, 6899086, 40888802, 168888169, 868862887, 884888909, 4088888618, 6898889086, 40888888618, 108088888891, 864888888892, 1928888888668, 16888888880873, 8848888888909, 40888888888802, 120888888888896, 968888888886830

Offset: 1

Author

G. L. Honaker, Jr., Nov 16 2019

Keywords

• nonn
• base

Examples

			a(1) = 76 because 76 = 2*2*19, and there is exactly one loop on each side of the equals sign.
a(2) = 166 because 166 = 2*83, and there are exactly two loops on each side of the equals sign, etc. Note that '8' contains two loops.
		

Links

• Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 76

Crossrefs

Cf. A000040, A001743.

Programs

Mathematica

cntLo[n_] := Plus @@ ({1,0,0,0,0,0,1,0,2,1}[[IntegerDigits[n] + 1]]);  cntF[n_] := Plus @@ (cntLo /@ First /@ FactorInteger[n]); a[n_] := Block[{k=1}, While[ cntLo[k] != n || cntF[k] != n || PrimeQ[k], k++]; k]; Array[a, 8] (* Giovanni Resta, Nov 18 2019 *)

Extensions

a(5)-a(10) from Chuck Gaydos

a(11)-a(24) from Giovanni Resta, Nov 18 2019