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A343738 a(n) is the smallest prime p > k such that p + k is a power of 2, where k = 2*n - 1, or 0 if no such prime exists. 0
3, 5, 11, 549755813881, 23, 53, 19, 17, 47, 109, 43, 41, 103, 37, 227, 97, 223, 16349, 2011, 89, 983, 536870869, 83, 977, 79, 461, 971, 73, 71, 197, 67, 193, 191, 524221, 443, 953, 439, 181, 179, 433, 431, 173, 130987, 937, 167, 421, 163, 929, 1951, 157 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

k = 2*n-1 is the n-th odd number; p is the smallest prime > k such that p+k is a power of 2. If the constraint "> k" were removed, sequence A096822 would result.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

For n=1, k = 2*n-1 = 1, and the smallest prime p > 1 such that p+1 is a power of 2 is 3, so a(1)=3.

For n=3, k=5, and the smallest prime p > 5 such that p+5 is a power of 2 is 11, so a(3)=11.

For n=4, k=7, and there is no prime in the sequence {2^4 - 7 = 9, 2^5 - 7 = 25, 2^6 - 7 = 57, ...} until 2^39 - 7 = 549755813881, so a(4) = 549755813881.

For n=55, k=109, and the smallest prime p > 109 such that p+109 is a prime is a(55) = 2^963 - 109 (a 290-digit number).

CROSSREFS

Cf. A096822.

Sequence in context: A079037 A281087 A101315 * A066541 A279728 A087122

Adjacent sequences:  A343735 A343736 A343737 * A343739 A343740 A343741

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jun 27 2021

STATUS

approved

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Last modified May 22 11:58 EDT 2022. Contains 353949 sequences. (Running on oeis4.)