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A242109
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First of two consecutive (primes of the form n^2+1) with no semiprime of the same form between them.
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0
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2, 2917, 13457, 15377, 15877, 21317, 78401, 147457, 190097, 215297, 217157, 287297, 401957, 414737, 577601, 1299601, 1308737, 1313317, 1378277, 1547537, 1623077, 1664101, 1731857, 1742401, 1822501, 1887877, 1976837, 2044901, 2390117, 2421137, 2446097, 2483777
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2 is in the sequence because there is no semiprime between the two primes 1^2 + 1 = 2 and 2^2 + 1 = 5 of the form k^2 + 1.
2917 is in the sequence because there is no semiprime between the two primes 54^2 + 1 = 2917 and 56^2 + 1 = 3127 : 55^2 + 1 = 3026 = 2*17*89 is not a semiprime.
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MAPLE
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with(numtheory):nn:=2000: lst:={}:
for n from 1 to nn do:
if type(n^2+1, prime)=true
then
lst:=lst union {n}:
else
fi:
od:
n1:=nops(lst):
for m from 1 to n1-1 do:
i1:=lst[m]:i2:=lst[m+1]:ii:=0:
for k from i1+1 to i2-1 do:
x:=k^2+1:y:=factorset(x):
if bigomega(x)=2 and nops(y)=2
then
ii:=ii+1:
else
fi:
od:
if ii=0
then
printf(`%d, `, i1^2+1):
else
fi:
od:
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PROG
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(PARI)
for(n=1, 10^4, if(isprime(n^2+1), k=1; while(!isprime((n+k)^2+1), k++); c=0; for(i=1, k-1, d=factor((n+i)^2+1); s=sum(j=1, #d[, 1], d[j, 2]); if(s==2, c++; break)); if(c==0, print1(n^2+1, ", ")))) \\ Derek Orr, Aug 15 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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