A096823
a(n) = p*(p+(2n-1))/2, where p = A096822(n) is the smallest primes of form 2^x-(2n-1).
Original entry on oeis.org
6, 20, 12, 151115727449904501489664, 56, 40, 24, 272, 1504, 208, 176, 1312, 112, 80, 48, 6208, 992, 928, 2059264, 5696, 736, 144115176533131264, 608, 544, 5056, 416, 352, 4672, 224, 160, 96, 24704, 24448, 3904, 3776, 487936, 112384, 3392, 22912
Offset: 1
a(1) = 6 is the first even perfect number;
a(7) = 24 corresponds to A096821(1) = 24;
a(4) = 151115727449904501489664 = 2^38*(2^39-7) = 274877906944*549755813881;
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.
Original entry on oeis.org
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
Offset: 1
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).
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