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A145897 Starting prime (and 1): where number of consecutive squares m^2 satisfy r=p+4*m^2, prime 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

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).

PROG

(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

CROSSREFS

A145896 A145898 A145741

Sequence in context: A098059 A078860 A029710 * A078863 A263091 A320533

Adjacent sequences:  A145894 A145895 A145896 * A145898 A145899 A145900

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Oct 25 2008

STATUS

approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)