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 A158529 List of primes p with following properties: p = prime(n-1) for some n, p+7 is a square and is equal to prime(n+1)-1. 1
 29, 569, 1289, 41609, 147449, 2322569, 2842589, 7096889, 7485689, 10074269, 16208669, 21288989, 33802589, 54819209, 56610569, 57699209, 59814749, 115218749, 118069949, 126427529, 134235389, 149670749, 196448249, 240746249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: If the condition holds, prime(n-1) and prime(n) are twin primes of the form 10k+9 and 10k1+1, i.e. the last digits of the twin prime pairs are 9 and 1. The 9 ending is evident in this sequence. The table of the first 101 terms was computed using Zak Seidov's table. LINKS Cino Hilliard, List of n, a(n) for n=1..101 S. M. Ruiz, Integer then equal. Sebastian Martin Ruiz and others, Integers then Equals, digest of 7 messages in primenumbers Yahoo group, Mar 14 - Mar 20, 2009. Zak Seidov, A158470 first 101 terms. FORMULA Prime(n) is the n-th prime number. EXAMPLE For n = 11, prime(11-1)=29, 29+7=36; prime(11+1)=37, 37-1=36. So 29 is the first entry in the sequence. MATHEMATICA ppQ[{a_, b_}]:=Module[{s=Prime[a+1]-1}, IntegerQ[Sqrt[s]]&&b+7==s]; Select[ Table[ {n, Prime[n-1]}, {n, 2, 133*10^5}], ppQ][[All, 2]] (* Harvey P. Dale, Jul 31 2020 *) PROG (PARI) \\Copy and paste the Zak's file to zaklist.txt and edit to a straight \\list with CR after each entry. Start a new Pari sesion then \r zakilist.txt integerequal(a, b) = { local(x, p1, p2); for(j=1, 101, x=eval(concat("%", j)); p1=prime2(x-1); if(issquare(p1+a), p2=prime2(x+1); if((p1+a)==(p2-b), print1(p1", ") ) prime2(n) = \\the n-th prime using c:\sieve\prime.exe calling 8byte binary \\g:\sievedata\prime2-1trill.bin" 300 gig file of primes <10^12 { local(x, s); s=concat("c:/sieve/prime ", Str(n)); s=concat(s, " > temp.txt"); \\Must save to a temp file for correct output system(s); return(read("temp.txt")) } ) ) } CROSSREFS Sequence in context: A023948 A020974 A167740 * A020766 A069295 A103723 Adjacent sequences: A158526 A158527 A158528 * A158530 A158531 A158532 KEYWORD nonn AUTHOR Cino Hilliard, Mar 20 2009 EXTENSIONS Edited by N. J. A. Sloane Aug 31 2009 (rephrased definition, corrected offset). STATUS approved

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Last modified December 3 09:03 EST 2022. Contains 358515 sequences. (Running on oeis4.)