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A157495
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The first prime difference between the primes and their preceding squares.
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0
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2, 2, 5, 3, 2, 13, 13, 3, 7, 13, 31, 37, 5, 7, 11, 17, 23, 61, 3, 7, 37, 43, 2, 53, 61, 37, 3, 7, 73, 13, 127, 31, 37, 103, 5, 7, 13, 19, 23, 29, 79, 37, 47, 157, 53, 3, 67, 79, 2, 193, 37, 43, 97, 107, 61, 7, 13, 127, 241, 137, 139, 37, 163, 167, 277, 61, 7, 13, 23, 313, 29, 103
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If the only preceding square k such that p-k^2 is prime is 0, then we generate sequence A065377.
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EXAMPLE
| The 7-th prime is 17. The preceding squares of 17 are 16,9,4,1,0. The differences are
17-16=1, 17-9=8, 17-4=13, 17-1=16 and 17-0=17. Then 4 is the first preceding square
of 17 that can be subtracted from 17 to get a prime. So 13 is in the sequence. If we
decline the prime 13 in this fashion, we have 13-9=4,13-1=12,13-0=13. This shows
that 0 is the first square that can be subtract from 13 to get a prime number. So 13
is in the 6-th place in the sequence.
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PROG
| (PARI) g(n)= c=0; forprime(x=2, n, for(k=1, n^2, if(issquare(abs(x-k))&&isprime(k),
print1(k", "); c++; break))); c
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CROSSREFS
| Sequence in context: A076561 A132851 A146316 * A128134 A157223 A174608
Adjacent sequences: A157492 A157493 A157494 * A157496 A157497 A157498
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Mar 01 2009
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EXTENSIONS
| Definition and example clarified following a request from Zak Seidov. - Cino Hilliard (hillcino368(AT)hotmail.com), Apr 13 2009
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