A088787 Numbers which are primes and which remain prime for three successive applications of incrementing each digit by 2 with carries ignored.

61, 97, 227, 449, 661, 797, 881, 1307, 2797, 3877, 5477, 5657, 8297, 8669, 8849, 8861, 9887, 11257, 12517, 15287, 16487, 17387, 19427, 20287, 20897, 23197, 23957, 25717, 26227, 30637, 36947, 39217, 41687, 41927, 42197, 42797, 45127, 45827, 51637

Offset

1,1

Comments

Imagine that each digit of n is on a wheel on a combination lock and each wheel is being rotated two notches for each application of the function. Thus for the digits 0 to 7, the replacement digit is simply the digit+2, but for 8 the replacement digit is 0 and for 9 the replacement digit is 1. Thus 227 -> 449 -> 661 -> 883 -> 5 (initial zeros are dropped on results.)

Links

Table of n, a(n) for n=1..39.

Example

a(3)=227 because (i) 227 is prime and (ii) incrementing each digit of 227 by 2 yields 449 which is prime and (iii) incrementing each digit of 449 by 2 (ignoring carries) yields 661 which is prime and (iv) incrementing each digit of 661 by 2 yields 883 which is prime

Prog

Function Cycle222(long: p): long {i: integer; r: long; c: integer; for i=floor(log10(p)) to 0 step -1; c = floor(p/10^(i-1)) mod 10; r = r*10 + ((c+2) mod 10); next i; return r; } p=2; for i=1 to 90; n=sequence.count; do while sequence.count=n; j=cycle222(p); k=cycle222(j); if isprime(j) and isprime(k) and isprime(cycle222(k)) then sequence.add(p) else p=nextPrimeAfter(p); loop; next i;

Crossrefs

Cf. A088785, A088786, A088788.

Sequence in context: A144970 A045562 A104229 * A020350 A142108 A033239

Adjacent sequences: A088784 A088785 A088786 * A088788 A088789 A088790

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 16 2003

Status

approved