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A242109 First of two consecutive (primes of the form n^2+1) with no semiprime of the same form between them. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

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.

MAPLE

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:

PROG

(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

CROSSREFS

Cf. A002496, A005574.

Sequence in context: A114067 A109119 A002495 * A078457 A128148 A158348

Adjacent sequences:  A242106 A242107 A242108 * A242110 A242111 A242112

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 15 2014

STATUS

approved

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Last modified January 20 10:23 EST 2018. Contains 297960 sequences.