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A089392 Magnanimous primes: primes with the property that inserting a "+" in any place between two digits yields a sum which is prime. 11
2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 227, 229, 281, 401, 443, 449, 467, 601, 607, 647, 661, 683, 809, 821, 863, 881, 2221, 2267, 2281, 2447, 4001, 4027, 4229, 4463, 4643, 6007, 6067, 6803, 8009, 8221, 8821, 20261, 24407, 26881, 28429, 40427 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Original definition: Let the digits of n be abcd. Then bcd+a, cd+ab, d+abc, abcd, etc. must all be primes. If n is a k-digit number then it must produce k such primes.

Partition the digits of n into two groups by placing a '+' sign anywhere inside; the result of the expression is prime in every case. Conjecture: sequence is infinite. 11 is the largest term with all odd digits. 2 is the only member with all even digits. Observation: all two-digit primes with the most significant digit even are members.

In contradiction to the above conjecture, it is rather expected that this sequence is finite, cf. the link to C. Rivera's "Puzzle 401", and G. Resta's web page. Concerning the statement about 2 and 11, one can say that all terms except 2, 11 and 101 consist of even digits followed by a final odd digit. - M. F. Hasler, Dec 25 2014

Primes among the magnanimous numbers A252996. - M. F. Hasler, Dec 25 2014

LINKS

Zak Seidov, Table of n, a(n) for n = 1..84

E. Angelini et al., Insert "+" and always get a prime, Dec

2014

G. Resta, magnanimous numbers, 2013.

C. Rivera, Puzzle 401. Magnanimous primes, 2007.

EXAMPLE

2267 is a member which gives primes 2+267 = 269, 22+67 = 89, 226+7 = 233 and 2267 itself.

MAPLE

with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=[[], seq([j], j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n, base, 10): fl:=0: for s in sch do m:=add(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-1)]): if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ", n) fi od od: # C. Ronaldo

MATHEMATICA

mpQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]; And@@PrimeQ[ Table[ FromDigits[Take[idn, i]]+FromDigits[Take[idn, -(len-i)]], {i, len}]]]; Select[Range[41000], mpQ] (* Harvey P. Dale, Nov 06 2013 *)

PROG

(PARI) is_A089392(n)={!for(i=1, #Str(n), ispseudoprime([1, 1]*(divrem(n, 10^i)))||return)} \\ M. F. Hasler, Dec 25 2014

CROSSREFS

Cf. A089393, A089394, A089695, A028834, A182175, A088134, A221699, A227823, A252996.

Sequence in context: A078403 A129945 A046704 * A089695 A070027 A207294

Adjacent sequences:  A089389 A089390 A089391 * A089393 A089394 A089395

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Nov 10 2003

EXTENSIONS

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

Comments edited by Zak Seidov, Jan 29 2013

Edited by M. F. Hasler, Dec 25 2014

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)