A219785 Primes not neighboring an 11-smooth number.

103, 137, 157, 173, 227, 229, 233, 277, 283, 311, 313, 317, 347, 367, 373, 389, 409, 443, 457, 467, 509, 521, 523, 547, 557, 563, 569, 571, 607, 613, 619, 643, 653, 677, 683, 691, 709, 733, 739, 743, 761, 773, 787, 797, 821, 823, 827, 829, 853, 857, 859, 877

Offset: 1

Author

Jonathan Vos Post, Nov 27 2012

Keywords

• nonn
• easy

Examples

			103 is in the sequence because it is prime and the closest 11-smooth numbers are 100 and 105, which differ from 103 by 3 and -2 respectively, neither being -1 or +1.
137 is in the sequence because it is prime and neither 137 - 1 = 136 = 2^3 * 17 nor 137 + 1 = 138 = 2 * 3 * 23 are 11-smooth.
		

Crossrefs

Cf. A000040, A002473, A051037, A051038, A080194, A219528, A219697.

Programs

Mathematica

mx = 2^10; t11 = Select[Sort[Flatten[Table[2^i 3^j 5^k 7^l 11^m, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, Log[5, mx]}, {l, 0, Log[7, mx]}, {m, 0, Log[11, mx]}]]], # <= mx &]; Complement[Prime[Range[PrimePi[mx]]], Union[Select[t11 + 1, PrimeQ], Select[t11 - 1, PrimeQ]]] (* T. D. Noe, Nov 27 2012 *)

Formula

Numbers k such that k is prime and k is neither (2^i * 3^j * 5^k * 7^l * 11^m) - 1 nor (2^i * 3^j * 5^k * 7^l * 11^m) + 1 for any i, j, k, l, m >= 0.