A078494 Primes occurring only once in their decade.

97, 113, 127, 149, 181, 211, 241, 293, 307, 367, 397, 419, 421, 457, 479, 487, 557, 587, 631, 661, 683, 691, 719, 727, 743, 773, 787, 797, 809, 811, 839, 863, 877, 907, 929, 937, 953, 967, 983, 1009, 1021, 1049, 1051, 1087, 1117, 1163, 1171, 1193, 1201, 1249

Offset: 1

Author

Cino Hilliard, Jan 04 2003

Keywords

• nonn
• easy
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078500.

Programs

Magma

&cat [PrimesInInterval(10*n+1, 10*n+9): n in [0..150] | IsOne(#PrimesInInterval(10*n+1, 10*n+9))]; // Bruno Berselli, Sep 05 2012

PARI

decade1pr(n1,n2) = { forstep(x=n1,n2,10, if(isprime(x+1) && !isprime(x+3) && !isprime(x+7) && !isprime(x+9), print1(x+1" ");); if(isprime(x+3) && !isprime(x+1) && !isprime(x+7) && !isprime(x+9), print1(x+3" ");); if(isprime(x+7) && !isprime(x+1) && !isprime(x+3) && !isprime(x+9), print1(x+7" ");); if(isprime(x+9) && !isprime(x+1) && !isprime(x+3) && !isprime(x+7), print1(x+9" ");); ); }

Formula

a(n) ~ n log n. In particular, most primes are in this sequence. - Charles R Greathouse IV, Sep 07 2012