A210475 Let p_(4,1)(m) be the m-th prime == 1 (mod 4). Then a(n) is the smallest p_(4,1)(m) such that the interval(p_(4,1)(m)*n, p_(4,1)(m+1)*n) contains exactly one prime == 1 (mod 4).

13, 13, 29, 13, 193, 97, 97, 277, 457, 1193, 109, 229, 937, 397, 349, 1597, 2137, 937, 5569, 5737, 2833, 1549, 6733, 7477, 5077, 3457, 877, 4153, 12277, 11113, 8689, 14029, 11113, 5233, 24109, 14737, 26713, 1297, 77797, 12097, 51577, 57973, 33409, 30493, 49429, 112237, 10333, 143137

Offset: 2

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 23 2013

Keywords

• nonn

Comments

The limit of a(n) as n goes to infinity is infinity.

Conjecture: for n >= 12, every a(n) is the lesser of a pair of cousin primes p and p+4, (see A023200).

Crossrefs

Cf. A195325, A207820, A210465, A210467.

Programs

Mathematica

myPrime=Select[Table[Prime[n],{n,3000000}],Mod[#,4]==1&];
binarySearch[lst_,find_]:=Module[{lo=1,up=Length[lst],v},(While[lo<=up,v=Floor[(lo+up)/2];If[lst[[v]]-find==0,Return[v]];If[lst[[v]]0&]]]+offset-1]];
z=1;(*contains exactly ONE myPrime in the interval*)
Table[myPrime[[NestWhile[#1+1&,1,!((nextMyPrime[n myPrime[[#1]],z+1]>n myPrime[[#1+1]]))&]]],{n,2,30}]