A145898 -id:A145898 - cp's OEIS frontend

A145896 Values of m: where m^2 begins a run of consecutive squares satisfying r=p+4*m^2 with a sequence of primes.

3, 6, 2, 1, 8, 4, 7, 1, 2, 1, 1, 1, 19, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 2, 2, 1, 7, 3, 4, 1, 1, 2, 7, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2

Offset: 1

Enoch Haga, Oct 25 2008

Suggested by Farideh Firoozbakht's Puzzle 464 in Carlos Rivera's The Prime Puzzles & Problems Connection

			a(1)=3 because when m is 3 a sequence of three values of r end with prime 37; then 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 m, 4, does not produce a prime because r=1+4*4^2=65). For this one value 1 is assumed prime.

A145897 A145898 A145741

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

A145897 Starting prime (and 1): where number of consecutive squares m^2 satisfy r=p+4*m^2, prime.

Original entry on oeis.org

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

Offset: 1

Enoch Haga, Oct 25 2008

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.

This looks like (apparent from the ad-hoc introduced leading 1) an erroneous version of A023200, because the definition says that it registers prime chains p+4*m^2, m=1,2,3,.. but apparently does not consider whether m is actually larger than 1. So 3 should be in the sequence because 3+4*1^2 is prime. - R. J. Mathar, Mar 25 2024

			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).

Cf. A145896, A145898, A145741, A049492.

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

cp's OEIS Frontend

A145896 Values of m: where m^2 begins a run of consecutive squares satisfying r=p+4*m^2 with a sequence of primes.

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