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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). 3
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 (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: for n >= 12, every a(n) is the lesser of a pair of cousin primes p and p+4, (see A023200).

LINKS

Table of n, a(n) for n=2..49.

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]]<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.

Sequence in context: A166545 A022347 A026907 * A304268 A214466 A302678

Adjacent sequences:  A210472 A210473 A210474 * A210476 A210477 A210478

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)