A158756 -id:A158756 - cp's OEIS frontend

A158846 Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5).

19, 29, 41, 47, 53, 59, 61, 97, 149, 167, 173, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 499, 509, 521, 557, 563, 593, 641, 677, 743, 761, 797, 827, 887, 911, 941, 953, 1013, 1019, 1021, 1039, 1051, 1129, 1171, 1237, 1279, 1291

Offset: 1

Vladimir Shevelev, Mar 28 2009

nonn

We iteratively scan integer intervals (2^(m-1)..2^m), first the one with m=5, then m=6, m=7, etc., and start with the set S={3,5,7,11,...} of all odd primes. For each prime p = 2^m-k, 2^(m-1) < p < 2^m, p is removed from S if k is in S. Basically, all the upper primes of primes pairs are removed when the prime pair sums to a power of 2 which are larger than 2^4. The sequence shows all p that are removed from S at any stage m.

Powers 2^m, m >= 5, are not expressible as sums of two primes which are not in the sequence.

Cf. A156284, A158756, A156759.

A158846 := proc()
        local mmax,prrem,m,prm,pi,p,q ;
        mmax := 12 ; prrem := {} ;
        for m from 5 to mmax do
                prm := {} ;
                for pi from 1 do
                        k := ithprime(pi) ;
                        p := 2^m-k ;
                        if p <= 2^(m-1) then  break; end if;
                        if isprime(p) and not k in prrem then prm := prm union {p} ;
                        end if ;
                end do:
                prrem := prrem union prm ;
        end do: print( sort(prrem)) ; return ;
end proc:
A158846() ; # R. J. Mathar, Dec 07 2010

A158759 Removed primes according to algorithm of A156284 beginning with m=4.

Original entry on oeis.org

11, 13, 29, 41, 47, 59, 61, 97, 109, 149, 167, 173, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 509, 521, 557, 563, 593, 641, 677, 743, 761, 797, 827, 887, 911, 941, 953, 971, 1019, 1021, 1039, 1051, 1129, 1171, 1237, 1279, 1291, 1297, 1321

Offset: 1

Vladimir Shevelev, Mar 25 2009

nonn

Powers 2^m, m>=4, are not expressible as sums of two primes which are not in the sequence

A156284 A158756

A158847 Removed primes according to algorithm of A156284 beginning with m=6.

Original entry on oeis.org

41, 47, 53, 59, 61, 97, 109, 149, 167, 173, 227, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 499, 509, 521, 557, 563, 593, 641, 677, 743, 761, 827, 887, 911, 941, 953, 1013, 1019, 1021, 1039, 1051, 1129, 1171, 1237, 1279, 1291, 1297

Offset: 1

Vladimir Shevelev, Mar 28 2009

Powers 2^m, m>=6, are not expressible as sums of two primes which are not in the sequence

A156284 A158756 A158759 A158846

A158848 Prime numbers p where 2^k-p is prime, with k>6 and minimal.

Original entry on oeis.org

67, 97, 109, 149, 167, 173, 197, 227, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 499, 509, 521, 557, 563, 593, 641, 677, 743, 761, 773, 797, 827, 857, 887, 911, 941, 953, 971, 977, 983, 1013, 1019, 1021, 1039, 1051, 1129, 1171, 1237, 1279, 1291, 1297, 1321

Offset: 1

Vladimir Shevelev, Mar 28 2009

nonn

These are the primes removed according to algorithm of A156284 beginning with m=7.

Powers 2^m, m>=7, are not expressible as sums of two primes which are not in the sequence.

Bill McEachen, Table of n, a(n) for n = 1..10000

Cf. A152451, A156284, A158756, A158759, A158846, A158847, A086081.

isok(p) = if (isprime(p), my(k=ceil(log(p)/log(2))); (k >= 7) && isprime(2^k-p)); \\ Michel Marcus, Jan 22 2023

a(n) = A086081(n+11). - Bill McEachen, Jan 22 2023

Missing terms 773, 797, 827, 857 added by Michel Marcus, Jan 23 2023

New name from Bill McEachen, Jan 22 2023

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A158846 Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5).

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A158759 Removed primes according to algorithm of A156284 beginning with m=4.

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A158847 Removed primes according to algorithm of A156284 beginning with m=6.

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A158848 Prime numbers p where 2^k-p is prime, with k>6 and minimal.

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