login
Primes in A373805 in order of their occurrence.
4

%I #32 Aug 14 2024 21:44:08

%S 3,7,103,43,131,83,109,1889,181,199,55807,1289,2927,419,457,463,971,

%T 523,1091,563,617,159233,761,1549,821,839,6959,919,937,971,2003,1039,

%U 17793023,1279,1297,10513,11087,5849,12143,3181,1685503,3541,58943,3877,15887,2039,2069,8377,2141,2179,2304770047

%N Primes in A373805 in order of their occurrence.

%C The next prime after 169159 is not presently known.

%C 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 From _Michael De Vlieger_, Aug 12 2024: (Start)

%C See link for decimal expansion of a(320) = 21167 * 2^6095 + 1, a number with 1840 decimal digits.

%C a(607) = A373805(11585) = 1971503; no other primes seen for n <= 2^16. (End)

%H 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 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/sierp.html">The SierpiƄski Problem: Definition and Status</a>

%H Michael De Vlieger, <a href="/A373806/a373806.txt">Decimal expansion of A373805(8475) = a(320)</a>, bfile format with offset 1.

%H Michael De Vlieger, <a href="/A373806/a373806_1.txt">Table of n, a(n) for n = 321..607</a>

%t 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 (Python) # uses imports and A373805_gen in A373805

%o def agen(): # generator of terms

%o yield from (ai for i, ai in enumerate(A373805_gen(), 1) if isprime(ai))

%o print(list(islice(agen(), 51))) # _Michael S. Branicky_, Aug 12 2024

%Y Cf. A373805, A373807.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Aug 11 2024