A220220 -id:A220220 - cp's OEIS frontend

A161671 a(n) = prime(n) - A141468(n).

2, 2, 1, 1, 3, 4, 7, 7, 9, 14, 15, 19, 21, 22, 25, 29, 34, 35, 40, 43, 43, 47, 50, 55, 62, 65, 65, 68, 69, 71, 83, 86, 91, 91, 100, 101, 106, 111, 113, 118, 123, 124, 133, 133, 135, 136, 147, 158, 161, 161, 164, 169, 169, 177, 182, 187, 192, 193, 197, 200, 201, 209

Offset: 1

Juri-Stepan Gerasimov, Jun 16 2009, Dec 03 2009

nonn

			2(=2-0), 2(=3-1), 1(=5-4), 1(=7-6), 3(=11-8), 4(=13-9), 7(=17-10), 7(=19-12), 9(=23-14), 14(=29-15), etc.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Scatterplot of a(n), n = 1..120, showing and labeling primes p (in A214627) in red and blue, the red primes are duplicated and are listed in A220220. We plot in green duplicated composite terms.

Cf. A000040, A002808, A141468, A141559, A168563, A214627, A220220.

A161671 := proc(n)
    ithprime(n)-A141468(n) ;
end proc: # R. J. Mathar, Aug 08 2012

f[n_] := FixedPoint[n + PrimePi@ # &, n + PrimePi@ n]; Array[Prime[#] - f[# - 1] &, 62] (* Michael De Vlieger, Mar 22 2022, after Robert G. Wilson v at A141468 *)

a(n) = A000040(n) - A141468(n).
a(n+2) = A168563(n).
a(n) = A000040(n) - A018252(n-1), if n >= 2. - Omar E. Pol, Oct 21 2011
a(n) ~ n log n. - Charles R Greathouse IV, Dec 21 2011

Edited by N. J. A. Sloane, Jun 30 2009
207 replaced with 209 by R. J. Mathar, Oct 04 2009
Edited by Omar E. Pol, Oct 21 2011

A214627 Primes in A161671.

Original entry on oeis.org

2, 3, 7, 19, 29, 43, 47, 71, 83, 101, 113, 193, 197, 229, 241, 271, 283, 293, 311, 347, 383, 439, 457, 463, 491, 499, 523, 587, 619, 643, 683, 733, 797, 827, 857, 863, 919, 991, 1021, 1031, 1091, 1151, 1187, 1289, 1367, 1549, 1567, 1619, 1637, 1693, 1697, 1733, 1741, 1811, 1867, 1871, 1907

Offset: 1

Juri-Stepan Gerasimov, Aug 08 2012

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Scatterplot of A161671(n), n = 1..120, showing and labeling primes p in this sequence in red and blue. The red primes are duplicated and are listed in A220220. We plot in green duplicated composite terms.

Cf. A141468, A161671, A220220.

isA214627 := proc(n)
        if isprime(n) then
                for j from 1 do
                        if A161671(j) = n then
                                return true;
                        elif j >7 and A161671(j) > n then
                                return false;
                        end if;
                end do:
        else
                false;
        end if;
end proc:
for n from 2 to 2000 do
        if isA214627(n) then
                printf("%d,",n) ;
        end if;
end do; # R. J. Mathar, Aug 09 2012

f[n_] := FixedPoint[n + PrimePi@ # &, n + PrimePi@ n]; Union@ Reap[Do[If[PrimeQ[#], Sow[#]] &[Prime[i] - f[i - 1] ], {i, 350}] ][[-1, -1]] (* Michael De Vlieger, Mar 22 2022, after Robert G. Wilson v at A141468 *)

A161671 INTERSECT A000040.

cp's OEIS Frontend

A161671 a(n) = prime(n) - A141468(n).

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