This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373806 #32 Aug 14 2024 21:44:08
%S A373806 3,7,103,43,131,83,109,1889,181,199,55807,1289,2927,419,457,463,971,
%T A373806 523,1091,563,617,159233,761,1549,821,839,6959,919,937,971,2003,1039,
%U A373806 17793023,1279,1297,10513,11087,5849,12143,3181,1685503,3541,58943,3877,15887,2039,2069,8377,2141,2179,2304770047
%N A373806 Primes in A373805 in order of their occurrence.
%C A373806 The next prime after 169159 is not presently known.
%C A373806 Added Aug 14 2024: it is 123287*2^m + 1, where m = 2538167. See the Ballinger-Keller link. More details will be added soon. - _N. J. A. Sloane_, Aug 14 2024
%C A373806 From _Michael De Vlieger_, Aug 12 2024: (Start)
%C A373806 See link for decimal expansion of a(320) = 21167 * 2^6095 + 1, a number with 1840 decimal digits.
%C A373806 a(607) = A373805(11585) = 1971503; no other primes seen for n <= 2^16. (End)
%H A373806 N. J. A. Sloane, <a href="/A373806/b373806.txt">Table of n, a(n) for n = 1..319</a> [a(320) is too large to include - see _Michael De Vlieger_'s comment and links]
%H A373806 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/sierp.html">The Sierpiński Problem: Definition and Status</a>
%H A373806 Michael De Vlieger, <a href="/A373806/a373806.txt">Decimal expansion of A373805(8475) = a(320)</a>, bfile format with offset 1.
%H A373806 Michael De Vlieger, <a href="/A373806/a373806_1.txt">Table of n, a(n) for n = 321..607</a>
%t A373806 nn = 2^14; s = j = 1; Reap[Monitor[Do[If[PrimeQ[j], Sow[j]; s = -s; k = Prime[n] + s, k = 2 j + s]; j = k, {n, 2, nn}], n] ][[-1, 1]] (* _Michael De Vlieger_, Aug 12 2024 *)
%o A373806 (Python) # uses imports and A373805_gen in A373805
%o A373806 def agen(): # generator of terms
%o A373806 yield from (ai for i, ai in enumerate(A373805_gen(), 1) if isprime(ai))
%o A373806 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Aug 12 2024
%Y A373806 Cf. A373805, A373807.
%K A373806 nonn
%O A373806 1,1
%A A373806 _N. J. A. Sloane_, Aug 11 2024