A329590 Odd numbers k that cannot be expressed as k = p+q+r, with p prime and (q, r) a pair of twin primes.

1, 3, 5, 7, 9, 33, 57, 93, 99, 129, 141, 153, 177, 183, 195, 213, 225, 243, 255, 261, 267, 273, 297, 309, 327, 333, 351, 369, 393, 411, 423, 435, 453, 477, 489, 501, 513, 519, 525, 537, 561, 573, 591, 597, 603, 633, 645, 657, 663, 675, 687, 693, 705, 711, 723

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Example

33 can be expressed as the sum of three primes in 9 different ways:
33 = 11 + 11 + 11 = 13 + 13 + 7 = 17 + 11 + 5 = 17 + 13 + 3 = 19 + 7 + 7 = 19 + 11 + 3 = 23 + 5 + 5 = 23 + 7 + 3 = 29 + 2 + 2;
there is no pair of twin primes in the addends, so 33 is a term.

Prog

(PARI) for(n = 0, 500, m = 2*n+1; v = 0; forprime(i = 3, m-8, j = (m-i)/2; if(isprime(j-1) && isprime(j+1), v = 1)); if(v == 0, print1(m, ", ")))
(PARI) isok(k) = {if (! (k % 2), return (0)); forprime(p=3, k, if (isprime((k-p)\2-1) && isprime((k-p)\2+1), return(0)); ); return (1); } \\ Michel Marcus, Feb 16 2020

Crossrefs

Cf. A001359, A034961, A054735, A068307, A124868.

Sequence in context: A131668 A119252 A283003 * A141708 A081434 A007632

Adjacent sequences: A329587 A329588 A329589 * A329591 A329592 A329593

Keyword

nonn

Author

Antonio Roldán, Feb 13 2020

Status

approved