A156038 -id:A156038 - cp's OEIS frontend

A114977 Numbers k such that (j^k + k^j) == 0 (mod k+j), j=2 case.

1, 2, 8, 128, 2144, 4808, 12872, 14168, 32377, 33672, 45992, 116192, 185768, 186824, 271208, 426008, 484177, 524288, 601352, 612768, 755792, 996032, 1878368, 2262752, 3094247, 4325960, 4810808, 6331808, 6707352, 10037792, 10908137, 11475128, 12672992, 13705232

Offset: 1

Zak Seidov, Feb 22 2006

nonn

From Robert G. Wilson v, Aug 02 2021: (Start)
Prime terms: 2, then A156048.
The exponents of the powers of two which are terms: 0, 1, then A014741(n)+1.
The vast majority of terms are congruent to 8 (mod 24); no terms are congruent to 4 (mod 6) nor to 3 (mod 10).
(End)

Robert G. Wilson v, Table of n, a(n) for n = 1..1189 (first 645 terms from Hiroaki Yamanouchi).

Cf. A156038 (odd terms), A156048 (odd prime terms).

Cf. A014741, A114978, A114979, A114980, A114981.

fQ[n_] := PowerMod[2, n, n + 2] + 2 == n; Select[ Range[10^7], fQ] (* Robert G. Wilson v, Aug 02 2021 *)

isok(n, k=2) = (k^n+n^k) % (n+k) == 0; \\ Michel Marcus, Oct 10 2013

is(n)=Mod(2, n+2)^n==-4 \\ Charles R Greathouse IV, Oct 19 2013

a(9)-a(22) from Michel Marcus, Oct 10 2013

a(23)-a(34) from Hiroaki Yamanouchi, Sep 26 2015

A156048 Odd prime numbers p with the property that (2^p + p^2) == 0 (mod (p+2)).

Original entry on oeis.org

32377, 10908137, 34030327, 4860035567, 7656800897, 13398374537, 41162676047, 49277997407, 169906146727, 429221023247, 517971170207, 1587472376807, 1692526508927, 2687542461767, 2827976112047, 2918988711407, 3538852646177, 3843606175697, 3868058416007, 4090897510247

Offset: 1

Zak Seidov, Oct 31 2009

nonn

Subsequence of A114977 and of A156038. - Michel Marcus, Oct 19 2013

Giovanni Resta, Table of n, a(n) for n = 1..31 (terms < 10^13)

Cf. A114977, A156038.

isok(n) = isprime(n) && (n != 2) && ((2^n+n^2)% (n+2) == 0); \\ Michel Marcus, Oct 19 2013

is(n)=Mod(2,n+2)^n==-4 && n>2 && isprime(n) \\ Charles R Greathouse IV, Oct 19 2013

a(5) from Zak Seidov, Oct 31 2009
a(6)-a(8) from Juri-Stepan Gerasimov, Jan 16 2020
Terms a(9) and beyond from Giovanni Resta, Jan 23 2020

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A114977 Numbers k such that (j^k + k^j) == 0 (mod k+j), j=2 case.

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A156048 Odd prime numbers p with the property that (2^p + p^2) == 0 (mod (p+2)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

PARI

Extensions