A122764 Initial terms of arithmetic progression of primes in A005115 with duplicates removed.

2, 3, 5, 7, 199, 110437, 4943, 31385539, 115453391, 53297929, 3430751869, 4808316343, 8297644387, 214861583621, 5749146449311

Offset: 1

Author

Roger L. Bagula, Sep 22 2006

Keywords

• nonn
• less

Comments

Old title was: "In A005115 a+b*j: the a term with duplicates removed."

If duplicate terms are not removed, we obtain A113827. - Charlie Neder, Feb 02 2019

Examples

			A005115(7) comes from the 7-term prime progression {7, 157, 307, 457, 607, 757, 907}, and so 7 is in this sequence. - _Charlie Neder_, Feb 02 2019
		

Links

• Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, Pages 481-547 from Volume 167 (2008), Issue 2.

Crossrefs

Cf. A093364, A005115.

Programs

Mathematica

a = {{ 1, 2, 2}, {2, 2 + j, 3}, {3, 3 + 2j, 7}, {4, 5 + 6j, 23}, {5, 5 + 6j, 29}, {6, 7 + 30j, 157}, {7, 7 + 150j, 907}, {8, 199 + 210j, 1669}, {9, 199 + 210j, 1879}, {10, 199 + 210j, 2089}, {11, 110437 + 13860j, 249037}, {12, 110437 + 13860j, 262897}}
Union[Table[CoefficientList[a[[n, 2]], j][[1]], {n, 1, 12}]]

Extensions

Better name and a(7)-a(15) from Charlie Neder, Feb 02 2019