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 A303550 Numbers n such that abs(60n^2 - 1710n + 12150) +- 1 are twin primes. 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 27, 33, 34, 35, 36, 38, 41, 50, 56, 57, 64, 66, 69, 75, 81, 85, 86, 90, 93, 98, 103, 106, 119, 121, 133, 136, 141, 143, 146, 150, 181, 182, 189, 195, 202, 207, 208, 212, 215, 218, 219, 225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The formula was discovered by Andrew T. Gazsi in 1961. The polynomial can also be given as 30(2n - 27)(n - 15). Its value is negative (-30) at n = 14 and 0 and n = 15. Beiler erroneously claimed that the polynomial generates twin primes for n = 1 to 20. REFERENCES Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, 2nd ed., Dover Publications, Inc., New York, 1966, p. 225. Joseph B. Dence and Thomas P. Dence, Elements of the Theory of Numbers, Academic Press, 1999, problem 1.94, p.35. Andrew T. Gazsi, A Formula to Generate Prime Pairs, Recreational Mathematics Magazine, edited by Joseph S. Madachy, Issue 6, December 1961, p. 44. LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 James Alston Hope Hunter and Joseph S. Madachy, Mathematical Diversions, D. van Nostrand Company, Inc., Princeton, New Jersey, 1963, p. 7. Carlos Rivera, Problem 44. Twin-primes producing polynomials race, The Prime Puzzles & Problems Connection. EXAMPLE 1 is in the sequence since 60*1^2 - 1710*1 + 12150 = 10500 and (10499, 10501) are twin primes. MAPLE filter:= proc(n) local k;   k:= abs(60*n^2-1710*n+12150);   isprime(k+1) and isprime(k-1) end proc: select(filter, [\$1..300]); # Robert Israel, Jun 19 2018 MATHEMATICA f[n_] := 60n^2 - 1710n + 12150; aQ[n_]:=PrimeQ[f[n]-1] && PrimeQ[f[n]+1]; Select[Range[225], aQ] PROG (PARI) f(n) = abs(60*n^2 - 1710*n + 12150); isok(n) = my(fn=f(n)); isprime(fn-1) && isprime(fn+1); \\ Michel Marcus, Apr 27 2018 CROSSREFS Cf. A001097, A001359, A006512, A088485, A108897, A124518, A124519, A139404, A185660. Sequence in context: A320230 A076564 A325044 * A164563 A179892 A061773 Adjacent sequences:  A303547 A303548 A303549 * A303551 A303552 A303553 KEYWORD nonn,easy AUTHOR Amiram Eldar, Apr 26 2018 STATUS approved

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Last modified October 23 20:17 EDT 2019. Contains 328373 sequences. (Running on oeis4.)