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Search: id:A145897
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| A145897 |
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Starting prime (and 1): where number of consecutive squares m^2 satisfy r=p+4*m^2, prime |
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+0
3
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| 1, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Suggested by Farideh Firoozbakht's Puzzle 464 in Carlos Rivera's The Prime Puzzles & Problems Connection. In this sequence Haga accepts 1 as a prime because then m^2 begins the first run of consecutive primes.
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EXAMPLE
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a(1)=1 because when there are 3 consecutive m^2, first prime is 5 and ending prime is 37: r=1+4*1^1=5, prime; and r=1+4*2^2=17, prime; and r=1+4*3^2=37, prime (and the next value of r does not produce a prime).
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PROGRAM
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(Other) UBASIC: 10 'p464 20 N=1 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 100 60 A=A+2 70 if A<=S then 40 80 M=M+1:R=N+4*M^2:if R=prmdiv(R) and M<100 then print N; R; M:goto 80 90 if M>=1 then stop 100 M=0:N=N+2:goto 30
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CROSSREFS
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A145896 A145898 A145741
Sequence in context: A098059 A078860 A029710 this_sequence A078863 A059351 A059262
Adjacent sequences: A145894 A145895 A145896 this_sequence A145898 A145899 A145900
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KEYWORD
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easy,nonn
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AUTHOR
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Enoch Haga (Enokh(AT)comcast.net), Oct 25 2008
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