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 A275114 Primes p for which the sum of the numbers in the Collatz iteration (A033493) of p is a prime. 0
 2, 67, 149, 163, 229, 359, 373, 401, 571, 719, 727, 827, 919, 941, 1031, 1049, 1129, 1153, 1201, 1283, 1307, 1319, 1433, 1453, 1627, 1637, 1987, 2017, 2089, 2137, 2237, 2267, 2281, 2351, 2543, 2617, 2731, 2819, 2851, 2861, 2927, 2969, 3191, 3253, 3581, 3671, 3719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes p such that A033493(p) is a prime. Prime terms from A225748. LINKS Eric Weisstein's World of Mathematics, Collatz Problem Wikipedia, Collatz conjecture EXAMPLE Prime 67 with Collatz trajectory (67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) is term because A033493(67) = 1459 (prime). MATHEMATICA Select[Prime@ Range@ 540, PrimeQ[Total@ FixedPointList[Which[# == 1, 1, EvenQ@ #, #/2, True, 3 # + 1] &, #] - 1] &] (* Michael De Vlieger, Jul 17 2016, after Alonso del Arte at A033493 *) PROG (MAGMA) [n: n in [1..4000] | IsPrime(&+[k eq 1 select n else IsOdd(Self(k-1)) and not IsOne(Self(k-1)) select 3*Self(k-1)+1 else Self(k-1) div 2: k in [1..5*n]]) and IsPrime(n)] CROSSREFS Cf. A033493, A225748. Sequence in context: A065721 A030472 A106998 * A217599 A107214 A174602 Adjacent sequences:  A275111 A275112 A275113 * A275115 A275116 A275117 KEYWORD nonn AUTHOR Jaroslav Krizek, Jul 17 2016 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)