A054987 Smallest composite x such that sigma(x+2^n) = sigma(x) + 2^n.

434, 305635357, 27, 39, 106645, 69, 2275, 63, 6475, 249, 7735, 3703, 10803, 16383, 58869, 51181, 87951, 1695, 9579, 105237, 98829, 1143369, 789609, 11625, 14038691, 178975, 48627929, 1881333, 402373721, 2667945, 82915599, 353195221, 70106601

Offset

1,1

Comments

The sequence is initiated by smallest of A015915. Special primes of A023202, A049488-A049491 also satisfy the Sigma[p+2^w]=Sigma[p]+2^w relation

Links

Table of n, a(n) for n=1..33.

Example

For the term 69: Sigma[69+2^6] = Sigma[133] = 1+7+19+133 = Sigma[69]+64 = (1+3+23+69)+64 = 160.

Mathematica

Table[ Select[ Range[ 1, 110000 ], Equal[ EulerPhi[ #+2^k ]-EulerPhi[ # ]-2^k, 0 ] &&!PrimeQ[ # ]& ], {k, 1, 22} ]

Prog

(PARI) a(n)=my(N=2^n, x=3); while(isprime(x++) || sigma(x+N) != sigma(x)+N, ); x \\ Charles R Greathouse IV, Mar 11 2014

Crossrefs

Cf. A049488-A049491, A001359, A054799, A015913, A015915, A023200, A023202, A054905.

Sequence in context: A259294 A050507 A145318 * A054905 A160353 A268475

Adjacent sequences: A054984 A054985 A054986 * A054988 A054989 A054990

Keyword

nonn

Author

Labos Elemer, May 29 2000

Extensions

More terms from Labos Elemer, Aug 14 2003

a(21) corrected and a(27)-a(33) from Donovan Johnson, Nov 30 2008

Status

approved