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A210476 Let p_(4,3)(m) be the m-th prime == 3 (mod 4). Then a(n) is the smallest p_(4,3)(m) such that the interval(p_(4,3)(m)*n, p_(4,3)(m+1)*n) contains exactly one prime == 3(mod 4). 2
7, 67, 43, 67, 67, 191, 883, 43, 643, 379, 739, 103, 463, 643, 487, 883, 1303, 3847, 1447, 13963, 1087, 8863, 1999, 8167, 7687, 8443, 2707, 2203, 11083, 3463, 7687, 31387, 8419, 15919, 12979, 10099, 26683, 22027, 46687, 79687, 15439, 65839, 46723, 44683, 14887, 58963, 13879, 26947, 77587 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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

Conjecture: every a(n), except for a(7) = 191, is the lesser of a pair of cousin primes p and p+4, (see A023200).

LINKS

Table of n, a(n) for n=2..50.

MATHEMATICA

myPrime=Select[Table[Prime[n], {n, 3000000}], Mod[#, 4]==3&];

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]]<find, lo=v+1, up=v-1]]; 0)];

myPrimeQ[n_]:=binarySearch[myPrime, n];

nextMyPrime[n_, offset_Integer:1]:=myPrime[[myPrimeQ[NextPrime[n, NestWhile[#1+1&, 1, !myPrimeQ[NextPrime[n, #1]]>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}]

CROSSREFS

Cf. A195325, A207820, A210465, A210467, A210475.

Sequence in context: A223889 A197744 A052351 * A217095 A106111 A261184

Adjacent sequences:  A210473 A210474 A210475 * A210477 A210478 A210479

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)