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A102278 Numbers n such that 78*10^n + 217 is prime. 3
1, 2, 8, 10, 13, 21, 22, 36, 57, 80, 149, 484, 505, 642, 806, 974, 1674 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n is a term greater than 2 in this sequence and m = 3*(78*10^n + 217) then phi(m) = reversal(m) (m is in the sequence A069215) because phi(m) = 2*(78*10^n + 216) = 156*10^n + 432 = reversal(234*10^n + 651) = reversal(m).

For example since 8>2 & 8 is in this sequence, for m = 3* (78*10^8 + 217) = 23400000651 phi(m) = reversal(m), so 23400000651 is a term of A069215.

Let f(n,m,r,t) = ((9)(n).78.(0)(m).21.(9)(n))(r).(9)(t).7 where dot between numbers means concatenation and "(m)(n)" means number of m's is n.

In fact I proved that for nonnegative integers n, m, r & t such that r*t = 0 if p = f(n,m,r,t) is prime then phi(3*p) = reversal (3*p). (3*p is in the sequence A069215, some special cases:

Case I, p = f(0,0,0,n-1) = (9)(n-1).7 = 10^n - 3 (see A089675). Case II, p = f(0,n-3,0,0) = 78.(0)(n-3).217 = 78*10^n + 217. Case III, p = f(0,0,n,0) = (7821)(n).7. In this case I found only three such prime p1 = (78217)(0).7 = 7, p2 = (7821)(2).7 = 782178217 & p3 = (7821)(674).7, p3 is a prime with length 2697.

Next term is greater than 8280.

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

8 is in the sequence because 78.(8-3)(0).217 = 7800000217 is prime.

MATHEMATICA

Do[If[PrimeQ[78*10^n + 217], Print[n]], {n, 8280}]

PROG

(PARI) is(n)=ispseudoprime(78*10^n+217) \\ Charles R Greathouse IV, May 22 2017

CROSSREFS

Cf. A089675, A069215, A085331, A101700.

Sequence in context: A176969 A303358 A176464 * A110961 A213535 A161349

Adjacent sequences:  A102275 A102276 A102277 * A102279 A102280 A102281

KEYWORD

more,nonn

AUTHOR

Farideh Firoozbakht, Jan 04 2005

STATUS

approved

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Last modified September 18 23:06 EDT 2020. Contains 337174 sequences. (Running on oeis4.)