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A054987
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Smallest composite x such that sigma(x+2^n) = sigma(x) + 2^n.
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4
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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For the term 69: Sigma[69+2^6] = Sigma[133] = 1+7+19+133 = Sigma[69]+64 = (1+3+23+69)+64 = 160.
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MATHEMATICA
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Table[ Select[ Range[ 1, 110000 ], Equal[ EulerPhi[ #+2^k ]-EulerPhi[ # ]-2^k, 0 ] &&!PrimeQ[ # ]& ], {k, 1, 22} ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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