A113827 -id:A113827 - cp's OEIS frontend

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

Roger L. Bagula, Sep 22 2006

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

			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

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

Cf. A093364, A005115.

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}]]

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

A260939 Thirteen primes in arithmetic progression with difference 60060 and minimal initial term.

Original entry on oeis.org

4943, 65003, 125063, 185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663

Offset: 1

Marco Ripà, Aug 05 2015

This sequence is 13 primes long and was discovered by W. N. Seredinsky.

			a(4) = 4943 + 3*60060 = 185123.

Jens Kruse Andersen, All known AP24 to AP26.
Wikipedia, Primes in arithmetic progression.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A002110, A033290, A113827, A260751.

[4943+(n-1)*60060: n in [1..13]]; // Bruno Berselli, Aug 10 2015

Table[4943 + (n - 1) 60060, {n, 1, 13}] (* Bruno Berselli, Aug 10 2015 *)

a(n)=60060*n-55117 \\ Charles R Greathouse IV, Aug 25 2017

[4943+(n-1)*60060 for n in (1..13)] # Bruno Berselli, Aug 10 2015

a(n) = 4943 + (n-1)*60060 = 4943 + (n-1)*2*A002110(6).

cp's OEIS Frontend

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

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