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 A054987 Smallest composite x such that sigma(x+2^n) = sigma(x) + 2^n. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 13 23:25 EDT 2024. Contains 371652 sequences. (Running on oeis4.)