A244917 -id:A244917 - cp's OEIS frontend

A248412 Smallest prime p such that p - 2^e is also prime power (A053810) in exactly n cases for nonnegative integers e.

149, 2, 5, 11, 83, 829, 3331, 32941, 176417, 854929, 2233531, 12699571, 47924959, 763597201

Offset: 0

Robert G. Wilson v, Oct 06 2014

nonn

first case when A115230 equals n.
149, 331, 373, 509, 701, 757, 809, 877, 907, 997, 1019, ...;
2, 3, 127, 163, 179, 191, 193, 223, 239, 251, 269, 311, ...;
5, 7, 23, 37, 47, 53, 59, 67, 71, 79, 97, 101, 103, ...;
11, 13, 17, 19, 29, 31, 41, 43, 61, 73, 89, 131, 137, ...;
83, 113, 139, 181, 199, 293, 353, 571, 593, 601, 619, ...;
829, 1217, 1487, 2131, 2341, 2551, 2971, 4051, 4261, ...;
3331, 12109, 14551, 17393, 18233, 22279, 22307, 22741, ...;
32941, 34369, 44029, 49433, 53633, 67189, 95717, 99833, ...;
176417, 304771, 314723, 314779, 349667, 414707, 451937, ...;
854929, 1297651, 1328927, 1784723, 2164433, 2488909, ...;
2233531, 6026089, 7475389, 7623229, 9644911, 10019551, ...;
12699571, 18464123, 52849879, 78127339, 79303579, 84397463, ...;
47924959, 153309649, 204797059, 248685923, 273865219, ...;
763597201, ...;
...

Cf. A115230, A244917, zeroth row A095842, first row A095841.

f[p_] := Length@ Table[q = p - 2^exp; If[ PrimeNu@ q == 1, {q}, Sequence @@ {}], {exp, 0, Floor@ Log2@ p}]; t = Table[0, {20}]; p = 2; While[p < 1000000000, a = f[p] +1; If[a < 101 && t[[a]] == 0, t[[a]] == p; Print[{a -1, p}]]; p = NextPrime@ p]; t

a(n) <= A244917(n) for n>0.

cp's OEIS Frontend

A248412 Smallest prime p such that p - 2^e is also prime power (A053810) in exactly n cases for nonnegative integers e.

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