A373805 -id:A373805 - cp's OEIS frontend

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

N. J. A. Sloane, Aug 11 2024

nonn

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)

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

Cf. A373805, A373807.

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 *)

# 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

A373807 Indices of prime terms in A373805.

Original entry on oeis.org

2, 4, 8, 10, 13, 15, 17, 23, 25, 27, 37, 41, 46, 48, 50, 52, 55, 57, 60, 62, 64, 74, 76, 79, 81, 83, 88, 90, 92, 94, 97, 99, 115, 117, 119, 124, 129, 133, 138, 141, 153, 156, 163, 166, 171, 173, 175, 179, 181, 183, 205, 207, 219, 224, 226, 236, 240, 245, 247, 250, 254, 258, 276, 278, 281, 283

Offset: 1

N. J. A. Sloane, Aug 11 2024

nonn

Please see the comments on A373805 and A373806 for further information.

a(608) > 65536. - Michael De Vlieger, Aug 12 2024

Michael De Vlieger, Table of n, a(n) for n = 1..607 (First 319 terms from N. J. A. Sloane)

Cf. A373805, A373806.

nn = 2^14; s = j = 1; Reap[Monitor[Do[If[PrimeQ[j], Sow[n - 1]; s = -s; k = Prime[n] + s, k = 2 j + s]; j = k, {n, 2, nn}], n] ][[-1, 1]] (* Michael De Vlieger, Aug 12 2024 *)

# uses imports and A373805_gen in A373805
def agen(): # generator of terms
    yield from (i for i, ai in enumerate(A373805_gen(), 1) if isprime(ai))
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 12 2024

A373808 If a(n-1) is not a prime, then a(n) = 2*a(n-1) + S; otherwise set S = -S and a(n) = prime(n) + S; start with a(1) = 2, S = -1.

Original entry on oeis.org

2, 4, 9, 19, 10, 19, 18, 37, 22, 43, 32, 65, 131, 42, 83, 54, 109, 60, 119, 237, 473, 945, 1889, 90, 181, 100, 199, 108, 217, 435, 871, 1743, 3487, 6975, 13951, 27903, 55807, 162, 323, 645, 1289, 182, 365, 731, 1463, 2927, 210, 419, 228, 457, 232, 463, 242, 485, 971, 262, 523, 272, 545, 1091, 282

Offset: 1

N. J. A. Sloane, Aug 12 2024

nonn

Similar to A373805, but with different initial values. Contains a repeated term (19), but that is allowed. Merges with A373805 at a(10) = 22. The primes here are therefore essentially the same as the primes in A373805: see A373806 and A373807.

N. J. A. Sloane, Table of n, a(n) for n = 1..5000

Cf. A373805, A373806, A373807.

Module[{n = 1, s = -1}, NestList[If[n++; PrimeQ[#], Prime[n] + (s = -s), 2*# + s] &, 2, 100]] (* Paolo Xausa, Aug 13 2024 *)

cp's OEIS Frontend

A373806 Primes in A373805 in order of their occurrence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A373807 Indices of prime terms in A373805.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A373808 If a(n-1) is not a prime, then a(n) = 2*a(n-1) + S; otherwise set S = -S and a(n) = prime(n) + S; start with a(1) = 2, S = -1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica