A373806 Primes in A373805 in order of their occurrence.

3, 7, 103, 43, 131, 83, 109, 1889, 181, 199, 55807, 1289, 2927, 419, 457, 463, 971, 523, 1091, 563, 617, 159233, 761, 1549, 821, 839, 6959, 919, 937, 971, 2003, 1039, 17793023, 1279, 1297, 10513, 11087, 5849, 12143, 3181, 1685503, 3541, 58943, 3877, 15887, 2039, 2069, 8377, 2141, 2179, 2304770047

Offset: 1

Author

N. J. A. Sloane, Aug 11 2024

Keywords

• nonn

Comments

The next prime after 169159 is not presently known.

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

From Michael De Vlieger, Aug 12 2024: (Start)

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

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

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..319 [a(320) is too large to include - see _Michael De Vlieger_'s comment and links]
• Ray Ballinger and Wilfrid Keller, The Sierpiński Problem: Definition and Status
• Michael De Vlieger, Decimal expansion of A373805(8475) = a(320), bfile format with offset 1.
• Michael De Vlieger, Table of n, a(n) for n = 321..607

Crossrefs

Cf. A373805, A373807.

Programs

Mathematica

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 *)

Python

# uses imports and A373805_gen in A373805
def agen(): # generator of terms
    yield from (ai for i, ai in enumerate(A373805_gen(), 1) if isprime(ai))
print(list(islice(agen(), 51))) # Michael S. Branicky, Aug 12 2024