A153352 -id:A153352 - cp's OEIS frontend

A255967 Odd numbers m that are neither of the form p + 2^k nor of the form p - 2^k with 2^k < m, k >= 1, and p prime.

1, 1973, 3181, 3967, 4889, 5617, 7747, 7913, 8363, 8587, 8923, 11437, 11993, 12517, 13285, 13973, 14101, 14231, 14489, 16117, 16769, 16849, 18391, 18611, 19583, 19819, 21289, 21683, 21701, 21893, 22147, 22817, 22949, 23651, 24943, 25829, 27197, 27437

Offset: 1

Arkadiusz Wesolowski, Mar 12 2015

nonn

Odd numbers m such that for all 2^k < m the numbers m + 2^k and m - 2^k are composite, with k >= 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A076335.
Subsequence of A006285. Supersequence of A256163.
A153352 gives the primes.

lst:=[]; for n in [1..27437 by 2] do t:=0; k:=0; while 2^k lt n do if IsPrime(n-2^k) or IsPrime(n+2^k) then t:=1; break; end if; k+:=1; end while; if IsZero(t) then Append(~lst, n); end if; end for; lst;

q[m_] :=  If[EvenQ[m], False, Module[{pow = 2},While[pow < m && !PrimeQ[m - pow] && !PrimeQ[m + pow], pow *= 2]; pow > m]]; Select[Range[30000], q] (* Amiram Eldar, Jul 19 2025 *)

isok(m) = if(!(m % 2), 0, my(pow = 2); while(pow < m && !isprime(m - pow) && !isprime(m + pow), pow *= 2); pow > m); \\ Amiram Eldar, Jul 19 2025

A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p2^k + 1, and p2^k - 1 are composite.

Original entry on oeis.org

8923, 24943, 35437, 42533, 52783, 83437, 105953, 116437, 126631, 133241, 145589, 164729, 172331, 192173, 204013, 215279, 254329, 304709, 308899, 398833, 430499, 436687, 454351, 476869, 479909, 483443, 497597, 522479, 527729, 529103, 545257, 561439, 562651

Offset: 1

Arkadiusz Wesolowski, Mar 20 2015

nonn

Subsequence of A256163.

Cf. A006285, A065381, A153352, A180247, A255967.

lst:=[]; for p in [3..562651 by 2] do if IsPrime(p) then t:=0; k:=0; while 2^k lt p do if IsPrime(p-2^k) or IsPrime(p+2^k) or IsPrime(p*2^k-1) or IsPrime(p*2^k+1) then t:=1; break; end if; k+:=1; end while; if IsZero(t) then Append(~lst, p); end if; end if; end for; lst;

A263645 Primes that are neither of the form p + 2^k nor of the form p - 2^k with k > 0, and p prime.

Original entry on oeis.org

2, 52504261, 55414847, 79933129, 152485283, 166441831, 177702619, 197903207, 199013093, 220403959, 226794259, 230701763, 245215801, 266642731, 304921637, 321979283, 335035097, 355404353, 359018299, 369810769, 388048561, 412590797, 445661719, 506400173, 540426473

Offset: 1

Arkadiusz Wesolowski, Oct 22 2015

nonn

Primes p such that for all k > 0 the numbers p + 2^k and p - 2^k are nonprimes.

Except for 2, this sequence is the intersection of A065381 and A137715.

Cf. A065381, A137715, A153352, A180247, A263644.

A281907 Numbers congruent to 47867742232066880047611079 modulo 66483034025018711639862527490.

Original entry on oeis.org

47867742232066880047611079, 66530901767250778519910138569, 133013935792269490159772666059, 199496969817288201799635193549, 265980003842306913439497721039, 332463037867325625079360248529, 398946071892344336719222776019, 465429105917363048359085303509

Offset: 1

Felix Fröhlich, Feb 01 2017

The terms of this sequence cannot be written as +-p^a +-q^b with p, q prime and a, b nonnegative integers for any possible choice of signs (cf. Theorem in Sun, 2000).

47867742232066880047611079 is a Brier number (A076335). - Jeppe Stig Nielsen, Sep 16 2020

Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comp. 29 (1975), 79-81.
Zhi-Wei Sun, On integers not of the form +-p^a+-q^b, Proceedings of the American Mathematical Society, Vol. 128, No. 4 (2000), 997-1002.

Cf. A153352.

Table[66483034025018711639862527490 n + 47867742232066880047611079, {n, 0, 7}] (* Michael De Vlieger, Feb 02 2017 *)

a(n) = 66483034025018711639862527490*n+47867742232066880047611079

a(n) = 66483034025018711639862527490*n + 47867742232066880047611079.

cp's OEIS Frontend

A255967 Odd numbers m that are neither of the form p + 2^k nor of the form p - 2^k with 2^k < m, k >= 1, and p prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p2^k + 1, and p2^k - 1 are composite.

Views

Author

Keywords

Crossrefs

Programs

Magma

A263645 Primes that are neither of the form p + 2^k nor of the form p - 2^k with k > 0, and p prime.

Views

Author

Keywords

Comments

Crossrefs

A281907 Numbers congruent to 47867742232066880047611079 modulo 66483034025018711639862527490.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

cp's OEIS Frontend

A255967 Odd numbers m that are neither of the form p + 2^k nor of the form p - 2^k with 2^k < m, k >= 1, and p prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p*2^k + 1, and p*2^k - 1 are composite.

Views

Author

Keywords

Crossrefs

Programs

Magma

A263645 Primes that are neither of the form p + 2^k nor of the form p - 2^k with k > 0, and p prime.

Views

Author

Keywords

Comments

Crossrefs

A281907 Numbers congruent to 47867742232066880047611079 modulo 66483034025018711639862527490.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p2^k + 1, and p2^k - 1 are composite.