A182719 Numbers of the form 5k + 4, 7k + 5, or 11k + 6.

4, 5, 6, 9, 12, 14, 17, 19, 24, 26, 28, 29, 33, 34, 39, 40, 44, 47, 49, 50, 54, 59, 61, 64, 68, 69, 72, 74, 75, 79, 82, 83, 84, 89, 94, 96, 99, 103, 104, 105, 109, 110, 114, 116, 117, 119, 124, 127, 129, 131, 134, 138, 139, 144, 145, 149, 152, 154, 159, 160, 164

Offset: 1

Author

Omar E. Pol, Feb 08 2011

Keywords

• nonn
• easy

Comments

Numbers such that the Ramanujan congruences apply, making p(a(n)) divisible by at least one of 5, 7, or 11, where p is A000041.

Union of A016897, A017041 and A017461.

First differences are periodic with period length 145.

Links

• Wikipedia, Ramanujan's congruences
• Index entries for linear recurrences with constant coefficients, order 146.

Crossrefs

Cf. A000041, A016897, A017041, A017461.

Programs

Magma

IsA182719:=func< n | exists{ k: k in [0..n div 5] | n in [5*k+4, 7*k+5, 11*k+6] } >; [ n: n in [1..160] | IsA182719(n) ]; // Klaus Brockhaus, Feb 08 2011

Mathematica

Union[With[{no=30},Join[5Range[0,no]+4,7Range[0,no]+5,11Range[0,no]+6]]]  (* Harvey P. Dale, Feb 18 2011 *)

Formula

a(n) = a(n-145) + 385 = a(n-1) + a(n-145) - a(n-146).

Extensions

Rewritten by Charles R Greathouse IV and Klaus Brockhaus, Feb 08 2011